## Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Non-investing personal finance issues including insurance, credit, real estate, taxes, employment and legal issues such as trusts and wills
markcoop
Posts: 796
Joined: Fri Mar 02, 2007 8:36 am

### Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Deciding between these 3 payment options to buy new car:
1) Pay full amount - get \$750 discount
2) 0% 36 months - no discount
3) 0.9% 60 months - no discount

Assuming I can afford either option, which do you think is best?

I believe the answer lies in what interest rate I can get for the money I am holding. In case 1, I earn a small amount of interest on the \$750 saved. In case 2, it's just the balance of the loan times the interest rate for each period. In case 3, it's the balance of the loan times the interest rate for each period minus the interest paid. Plugging in some numbers into a spread sheet, at a low interest rate (roughly below 1.5%) option 1 is best, at a middle interest rate (around 2%) option 2 is best and at a higher interest rate (roughly above 2.5%) option 3 is best.

Opinions?
Mark

John Z
Posts: 315
Joined: Sun Nov 14, 2010 5:42 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

My question is: what is the full amount price (not in dollars but is it the final negotiated price, sticker price, invoice price, etc.)? If you have already rec'd what you consider the lowest price that you could get I think you should get at least \$1000 discount assuming a mid-priced model. More if this is the sticker or so called invoice price. It's always nice to think about the money you'd make by not paying cash but chances are you would use the money for other items along the way. By paying cash you cannot use those dollars for other things.

FiveK
Posts: 5613
Joined: Sun Mar 16, 2014 2:43 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

markcoop wrote:
Wed Mar 21, 2018 1:50 pm
I believe the answer lies in what interest rate I can get for the money I am holding.
I believe you are correct. Gaze into your crystal ball, and....

Jags4186
Posts: 2480
Joined: Wed Jun 18, 2014 7:12 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Pay in full. This is 100% psychology.

Let's say you take out a 60 month loan on a \$30k car at 0%. That's \$500/mo. \$500 a month is easy to swallow when the car is brand new. But \$500/mo when the car is 4.5 years old, a few things start to break, you need to put tires on it, brakes need to be done, it's not as shiny anymore and the new car smell has worn off makes you start thinking "gee for \$500/mo I could be driving a lot nicer car." Next thing you know you have a brand new car.

inbox788
Posts: 5528
Joined: Thu Mar 15, 2012 5:24 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

How much is the car? Answer may be different for \$10k vs \$75k.

750/10k = 7.5%, 750/75k = 1%, 750/25k = 3%

For most balances, 0% for 36 months is likely the best answer.

Also, 0.9% x 5 years / 2 = 2.25% (total interest over linear estimate average balance). Around 1.5%+ this one might be the better long term deal.
Last edited by inbox788 on Wed Mar 21, 2018 2:54 pm, edited 1 time in total.

markcoop
Posts: 796
Joined: Fri Mar 02, 2007 8:36 am

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

inbox788 wrote:
Wed Mar 21, 2018 2:40 pm
How much is the car? Answer may be different for \$10k vs \$75k.

750/10k = 7.5%, 750/75k = 1%, 750/24k = 3%

For most balances, 0% for 36 months is likely the best answer.

Also, 0.9% x 5 years / 2 = 2.25% (total interest over linear estimate average balance).
Around \$30,000.

Not sure I understand what's the total interest over linear estimate average balance and how I would use it.
Mark

inbox788
Posts: 5528
Joined: Thu Mar 15, 2012 5:24 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

markcoop wrote:
Wed Mar 21, 2018 2:53 pm
inbox788 wrote:
Wed Mar 21, 2018 2:40 pm
How much is the car? Answer may be different for \$10k vs \$75k.

750/10k = 7.5%, 750/75k = 1%, 750/24k = 3%

For most balances, 0% for 36 months is likely the best answer.

Also, 0.9% x 5 years / 2 = 2.25% (total interest over linear estimate average balance).
Around \$30,000.

Not sure I understand what's the total interest over linear estimate average balance and how I would use it.
It's a simple interest calculation estimate. \$691 interest/ \$30k = 2.3% over the total life of the loan (5 years). This is your cost that you subtract from whatever your alternate investment total turns out to be. And in case where \$750 cash, you add interest earned and add it to your total gains. Begin with \$30k in a savings account and see how taking money out and putting it back into the savings account each month for 5 years changes based on your 3 choices. It's easy to figure out if savings account earns 0%. Try 5% and see that option 3 should be best. Around 1-2% it's about the same all around.

https://www.google.com/search?q=car+loan+calculator
Loan amount

30,000
\$
Interest rate (%)

0.9
Loan period (months)

60
Total cost of car loan\$30,691
Monthly payments\$512

Tal-
Posts: 348
Joined: Fri Apr 22, 2016 10:41 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

There aren't any bad options here.

Mathematically, you only need to return something like 1.3% to break even on a 750 discount after 3 years, or 1.6% for the five year option. This better than treasury bonds (~2.5%) and is lower than the expected returns from a diversified portfolio.

With that said, I would happily take the \$750 discount and pay cash. I tend to be open to debt, and even a fan of debt arbitrage in some situations like this - but I'd opt for the simplicity, peace of mind, and even pride that comes with simply owning the car outright.

My two cents.
Debt is to personal finance as a knife is to cooking.

soccerrules
Posts: 803
Joined: Mon Nov 14, 2016 4:01 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

I support #1 for these reasons from previous posts.

Pay in full. This is 100% psychology.
Let's say you take out a 60 month loan on a \$30k car at 0%. That's \$500/mo. \$500 a month is easy to swallow when the car is brand new. But \$500/mo when the car is 4.5 years old, a few things start to break, you need to put tires on it, brakes need to be done, it's not as shiny anymore and the new car smell has worn off makes you start thinking "gee for \$500/mo I could be driving a lot nicer car." Next thing you know you have a brand new car.

With that said, I would happily take the \$750 discount and pay cash. ......... but I'd opt for the simplicity, peace of mind, and even pride that comes with simply owning the car outright.
Don't let your outflow exceed your income or your upkeep will be your downfall.

JoeRetire
Posts: 1600
Joined: Tue Jan 16, 2018 2:44 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

markcoop wrote:
Wed Mar 21, 2018 1:50 pm
Deciding between these 3 payment options to buy new car:
1) Pay full amount - get \$750 discount
2) 0% 36 months - no discount
3) 0.9% 60 months - no discount

Assuming I can afford either option, which do you think is best?
"Best" is contextual. Don't decide any significant financial move in a vacuum.
Consider:

How much available cash do you have?
If withdrawing the \$30k brings you to zero, you might get a different answer than if you have \$2M.

If you will be withdrawing from invested funds, what rate are you currently getting?
If you get 6-7% on those investments, you might get a different answer than if you get 0.1-1%.

How long will you keep the car?
If you purchase a new car every 2 years, you might get a different answer than if you drive your cars until they die.

How debt averse are you?
If any debt leaves you lying awake sweating at night, you might get a different answer than if you often make moderate-risk investments and sleep well.

mega317
Posts: 2554
Joined: Tue Apr 19, 2016 10:55 am

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

And even when the math isn't strictly in favor of the loan, there are situations where additional liquidity could be worth paying a small premium for. I believe I have posted recently that when I bought a car I took out a cheap loan because I expected in the next few years a job change, move, and pregnancy. Fortunately all of those have now happened without significant hiccups, so I might pay the loan. Of course I can now beat the rate with risk-free investments so I might do that instead.

quantAndHold
Posts: 1780
Joined: Thu Sep 17, 2015 10:39 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Running time value of money calculations using a 1.5% interest rate for alternative investments, and a \$30,000 car gives this...
• cash - \$29,250
• 0% interest, 36 months - \$29,317
• 0.9% interest, 60 months - \$29,551
Higher interest rates, of course, favor taking a loan. At 2%, the best deal is the 0%, 36 month loan. At 2.5% and above, the 0.9%, 60 month loan becomes the best.

nura
Posts: 124
Joined: Mon Jun 27, 2016 11:24 am

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

markcoop wrote:
Wed Mar 21, 2018 1:50 pm
3) 0.9% 60 months - no discount
I would go with the third option for two reasons:
1) Liquidity: even if you have can pay off the car in cash today, you don't have to sell it if you ran out of cashflow to pay for essentials like food and shelter in the next 5 years.
2) Plenty of investments that will return 0.9% after taxes if you hold them for 5 years.

TSR
Posts: 704
Joined: Thu Apr 19, 2012 9:08 am

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Assuming there are no prepayment penalties, this would be a cash-flow question for me. I could afford to buy a \$25,000 car outright, but it would deplete my emergency fund to a level I would not feel great about. So perhaps I would take the 5-year loan, allowing me an extremely leisurely repayment schedule. I'd use that "leisure" to rebuild my savings, then I'd pay the whole thing off after six months or so. YMMV -- sounds like a lot of good options.

inbox788
Posts: 5528
Joined: Thu Mar 15, 2012 5:24 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Based on returns, 2% is about the break even point of indifference.
0% return, \$750 vs. \$0 vs. -\$691
1%, \$788 vs. \$481 vs. \$79
2%, \$828 vs. 1001 vs. \$902
5% \$962 vs. 2817 vs. 3714

Code: Select all

``````Savings	Loan	Payment	Month		Savings	Loan	Payment	Month		Savings	Loan	Payment	Month
\$750.00	0		0		\$30,000.00	30000	833.33	0		\$30,000.00	30000	511.52	0
\$750.00			1		\$29,166.67	29166.67	833.33	1		\$29,488.48	\$29,510.98	511.52	1
\$750.00			2		\$28,333.34	28333.34	833.33	2		\$28,976.96	\$29,021.59	511.52	2
\$750.00			3		\$27,500.01	27500.01	833.33	3		\$28,465.44	\$28,531.84	511.52	3
\$750.00			4		\$26,666.68	26666.68	833.33	4		\$27,953.92	\$28,041.72	511.52	4
\$750.00			5		\$25,833.35	25833.35	833.33	5		\$27,442.40	\$27,551.23	511.52	5
\$750.00			6		\$25,000.02	25000.02	833.33	6		\$26,930.88	\$27,060.37	511.52	6
\$750.00			7		\$24,166.69	24166.69	833.33	7		\$26,419.36	\$26,569.15	511.52	7
\$750.00			8		\$23,333.36	23333.36	833.33	8		\$25,907.84	\$26,077.56	511.52	8
\$750.00			9		\$22,500.03	22500.03	833.33	9		\$25,396.32	\$25,585.59	511.52	9
\$750.00			10		\$21,666.70	21666.7	833.33	10		\$24,884.80	\$25,093.26	511.52	10
\$750.00			11		\$20,833.37	20833.37	833.33	11		\$24,373.28	\$24,600.56	511.52	11
\$750.00			12		\$20,000.04	20000.04	833.33	12		\$23,861.76	\$24,107.49	511.52	12
\$750.00			13		\$19,166.71	19166.71	833.33	13		\$23,350.24	\$23,614.05	511.52	13
\$750.00			14		\$18,333.38	18333.38	833.33	14		\$22,838.72	\$23,120.24	511.52	14
\$750.00			15		\$17,500.05	17500.05	833.33	15		\$22,327.20	\$22,626.06	511.52	15
\$750.00			16		\$16,666.72	16666.72	833.33	16		\$21,815.68	\$22,131.51	511.52	16
\$750.00			17		\$15,833.39	15833.39	833.33	17		\$21,304.16	\$21,636.59	511.52	17
\$750.00			18		\$15,000.06	15000.06	833.33	18		\$20,792.64	\$21,141.30	511.52	18
\$750.00			19		\$14,166.73	14166.73	833.33	19		\$20,281.12	\$20,645.64	511.52	19
\$750.00			20		\$13,333.40	13333.4	833.33	20		\$19,769.60	\$20,149.60	511.52	20
\$750.00			21		\$12,500.07	12500.07	833.33	21		\$19,258.08	\$19,653.19	511.52	21
\$750.00			22		\$11,666.74	11666.74	833.33	22		\$18,746.56	\$19,156.41	511.52	22
\$750.00			23		\$10,833.41	10833.41	833.33	23		\$18,235.04	\$18,659.26	511.52	23
\$750.00			24		\$10,000.08	10000.08	833.33	24		\$17,723.52	\$18,161.73	511.52	24
\$750.00			25		\$9,166.75	9166.75	833.33	25		\$17,212.00	\$17,663.84	511.52	25
\$750.00			26		\$8,333.42	8333.42	833.33	26		\$16,700.48	\$17,165.56	511.52	26
\$750.00			27		\$7,500.09	7500.09	833.33	27		\$16,188.96	\$16,666.92	511.52	27
\$750.00			28		\$6,666.76	6666.76	833.33	28		\$15,677.44	\$16,167.90	511.52	28
\$750.00			29		\$5,833.43	5833.43	833.33	29		\$15,165.92	\$15,668.50	511.52	29
\$750.00			30		\$5,000.10	5000.1	833.33	30		\$14,654.40	\$15,168.73	511.52	30
\$750.00			31		\$4,166.77	4166.77	833.33	31		\$14,142.88	\$14,668.59	511.52	31
\$750.00			32		\$3,333.44	3333.44	833.33	32		\$13,631.36	\$14,168.07	511.52	32
\$750.00			33		\$2,500.11	2500.11	833.33	33		\$13,119.84	\$13,667.18	511.52	33
\$750.00			34		\$1,666.78	1666.78	833.33	34		\$12,608.32	\$13,165.91	511.52	34
\$750.00			35		\$833.45	833.45	833.33	35		\$12,096.80	\$12,664.26	511.52	35
\$750.00			36		\$0.12	0.12		36		\$11,585.28	\$12,162.24	511.52	36
\$750.00			37		\$0.12			37		\$11,073.76	\$11,659.84	511.52	37
\$750.00			38		\$0.12			38		\$10,562.24	\$11,157.07	511.52	38
\$750.00			39		\$0.12			39		\$10,050.72	\$10,653.92	511.52	39
\$750.00			40		\$0.12			40		\$9,539.20	\$10,150.39	511.52	40
\$750.00			41		\$0.12			41		\$9,027.68	\$9,646.48	511.52	41
\$750.00			42		\$0.12			42		\$8,516.16	\$9,142.19	511.52	42
\$750.00			43		\$0.12			43		\$8,004.64	\$8,637.53	511.52	43
\$750.00			44		\$0.12			44		\$7,493.12	\$8,132.49	511.52	44
\$750.00			45		\$0.12			45		\$6,981.60	\$7,627.07	511.52	45
\$750.00			46		\$0.12			46		\$6,470.08	\$7,121.27	511.52	46
\$750.00			47		\$0.12			47		\$5,958.56	\$6,615.09	511.52	47
\$750.00			48		\$0.12			48		\$5,447.04	\$6,108.53	511.52	48
\$750.00			49		\$0.12			49		\$4,935.52	\$5,601.59	511.52	49
\$750.00			50		\$0.12			50		\$4,424.00	\$5,094.27	511.52	50
\$750.00			51		\$0.12			51		\$3,912.48	\$4,586.57	511.52	51
\$750.00			52		\$0.12			52		\$3,400.96	\$4,078.49	511.52	52
\$750.00			53		\$0.12			53		\$2,889.44	\$3,570.03	511.52	53
\$750.00			54		\$0.12			54		\$2,377.92	\$3,061.19	511.52	54
\$750.00			55		\$0.12			55		\$1,866.40	\$2,551.97	511.52	55
\$750.00			56		\$0.12			56		\$1,354.88	\$2,042.36	511.52	56
\$750.00			57		\$0.12			57		\$843.36	\$1,532.37	511.52	57
\$750.00			58		\$0.12			58		\$331.84	\$1,022.00	511.52	58
\$750.00			59		\$0.12			59		-\$179.68	\$511.25	511.52	59
\$750.00			60		\$0.12			60		-\$691.20	\$0.11	511.52	60
``````

Code: Select all

``````Savings	Loan	Payment	Month		Savings	Loan	Payment	Month		Savings	Loan	Payment	Month
\$750.00	0		0		\$30,000.00	30000	833.33	0		\$30,000.00	30000	511.52	0
\$750.63			1		\$29,191.67	29166.67	833.33	1		\$29,513.48	\$29,510.98	511.52	1
\$751.25			2		\$28,382.67	28333.34	833.33	2		\$29,026.55	\$29,021.59	511.52	2
\$751.88			3		\$27,572.99	27500.01	833.33	3		\$28,539.22	\$28,531.84	511.52	3
\$752.50			4		\$26,762.64	26666.68	833.33	4		\$28,051.49	\$28,041.72	511.52	4
\$753.13			5		\$25,951.61	25833.35	833.33	5		\$27,563.34	\$27,551.23	511.52	5
\$753.76			6		\$25,139.90	25000.02	833.33	6		\$27,074.79	\$27,060.37	511.52	6
\$754.39			7		\$24,327.52	24166.69	833.33	7		\$26,585.83	\$26,569.15	511.52	7
\$755.01			8		\$23,514.47	23333.36	833.33	8		\$26,096.47	\$26,077.56	511.52	8
\$755.64			9		\$22,700.73	22500.03	833.33	9		\$25,606.70	\$25,585.59	511.52	9
\$756.27			10		\$21,886.32	21666.7	833.33	10		\$25,116.51	\$25,093.26	511.52	10
\$756.90			11		\$21,071.23	20833.37	833.33	11		\$24,625.93	\$24,600.56	511.52	11
\$757.53			12		\$20,255.46	20000.04	833.33	12		\$24,134.93	\$24,107.49	511.52	12
\$758.17			13		\$19,439.01	19166.71	833.33	13		\$23,643.52	\$23,614.05	511.52	13
\$758.80			14		\$18,621.88	18333.38	833.33	14		\$23,151.70	\$23,120.24	511.52	14
\$759.43			15		\$17,804.07	17500.05	833.33	15		\$22,659.48	\$22,626.06	511.52	15
\$760.06			16		\$16,985.57	16666.72	833.33	16		\$22,166.84	\$22,131.51	511.52	16
\$760.70			17		\$16,166.40	15833.39	833.33	17		\$21,673.79	\$21,636.59	511.52	17
\$761.33			18		\$15,346.54	15000.06	833.33	18		\$21,180.33	\$21,141.30	511.52	18
\$761.96			19		\$14,526.00	14166.73	833.33	19		\$20,686.46	\$20,645.64	511.52	19
\$762.60			20		\$13,704.77	13333.4	833.33	20		\$20,192.18	\$20,149.60	511.52	20
\$763.23			21		\$12,882.86	12500.07	833.33	21		\$19,697.49	\$19,653.19	511.52	21
\$763.87			22		\$12,060.27	11666.74	833.33	22		\$19,202.38	\$19,156.41	511.52	22
\$764.51			23		\$11,236.99	10833.41	833.33	23		\$18,706.86	\$18,659.26	511.52	23
\$765.14			24		\$10,413.02	10000.08	833.33	24		\$18,210.93	\$18,161.73	511.52	24
\$765.78			25		\$9,588.37	9166.75	833.33	25		\$17,714.59	\$17,663.84	511.52	25
\$766.42			26		\$8,763.03	8333.42	833.33	26		\$17,217.83	\$17,165.56	511.52	26
\$767.06			27		\$7,937.00	7500.09	833.33	27		\$16,720.66	\$16,666.92	511.52	27
\$767.70			28		\$7,110.29	6666.76	833.33	28		\$16,223.07	\$16,167.90	511.52	28
\$768.34			29		\$6,282.88	5833.43	833.33	29		\$15,725.07	\$15,668.50	511.52	29
\$768.98			30		\$5,454.79	5000.1	833.33	30		\$15,226.66	\$15,168.73	511.52	30
\$769.62			31		\$4,626.00	4166.77	833.33	31		\$14,727.83	\$14,668.59	511.52	31
\$770.26			32		\$3,796.53	3333.44	833.33	32		\$14,228.58	\$14,168.07	511.52	32
\$770.90			33		\$2,966.36	2500.11	833.33	33		\$13,728.92	\$13,667.18	511.52	33
\$771.54			34		\$2,135.50	1666.78	833.33	34		\$13,228.84	\$13,165.91	511.52	34
\$772.19			35		\$1,303.95	833.45	833.33	35		\$12,728.34	\$12,664.26	511.52	35
\$772.83			36		\$471.71	0.12		36		\$12,227.43	\$12,162.24	511.52	36
\$773.48			37		\$472.10			37		\$11,726.10	\$11,659.84	511.52	37
\$774.12			38		\$472.50			38		\$11,224.35	\$11,157.07	511.52	38
\$774.76			39		\$472.89			39		\$10,722.18	\$10,653.92	511.52	39
\$775.41			40		\$473.29			40		\$10,219.60	\$10,150.39	511.52	40
\$776.06			41		\$473.68			41		\$9,716.59	\$9,646.48	511.52	41
\$776.70			42		\$474.07			42		\$9,213.17	\$9,142.19	511.52	42
\$777.35			43		\$474.47			43		\$8,709.33	\$8,637.53	511.52	43
\$778.00			44		\$474.87			44		\$8,205.07	\$8,132.49	511.52	44
\$778.65			45		\$475.26			45		\$7,700.38	\$7,627.07	511.52	45
\$779.30			46		\$475.66			46		\$7,195.28	\$7,121.27	511.52	46
\$779.95			47		\$476.05			47		\$6,689.76	\$6,615.09	511.52	47
\$780.60			48		\$476.45			48		\$6,183.81	\$6,108.53	511.52	48
\$781.25			49		\$476.85			49		\$5,677.45	\$5,601.59	511.52	49
\$781.90			50		\$477.24			50		\$5,170.66	\$5,094.27	511.52	50
\$782.55			51		\$477.64			51		\$4,663.45	\$4,586.57	511.52	51
\$783.20			52		\$478.04			52		\$4,155.81	\$4,078.49	511.52	52
\$783.85			53		\$478.44			53		\$3,647.76	\$3,570.03	511.52	53
\$784.51			54		\$478.84			54		\$3,139.27	\$3,061.19	511.52	54
\$785.16			55		\$479.24			55		\$2,630.37	\$2,551.97	511.52	55
\$785.81			56		\$479.64			56		\$2,121.04	\$2,042.36	511.52	56
\$786.47			57		\$480.04			57		\$1,611.29	\$1,532.37	511.52	57
\$787.12			58		\$480.44			58		\$1,101.11	\$1,022.00	511.52	58
\$787.78			59		\$480.84			59		\$590.51	\$511.25	511.52	59
\$788.44			60		\$481.24			60		\$79.48	\$0.11	511.52	60
``````

Code: Select all

``````Savings	Loan	Payment	Month		Savings	Loan	Payment	Month		Savings	Loan	Payment	Month
\$750.00	0		0		\$30,000.00	30000	833.33	0		\$30,000.00	30000	511.52	0			\$0.00	\$0.00	\$0.00
\$751.25			1		\$29,216.67	29166.67	833.33	1		\$29,538.48	\$29,510.98	511.52	1			\$50.00	\$27.50	-\$22.50
\$752.50			2		\$28,432.03	28333.34	833.33	2		\$29,076.19	\$29,021.59	511.52	2			\$98.69	\$54.60	-\$44.10
\$753.76			3		\$27,646.09	27500.01	833.33	3		\$28,613.13	\$28,531.84	511.52	3			\$146.08	\$81.29	-\$64.79
\$755.01			4		\$26,858.84	26666.68	833.33	4		\$28,149.30	\$28,041.72	511.52	4			\$192.16	\$107.58	-\$84.58
\$756.27			5		\$26,070.27	25833.35	833.33	5		\$27,684.70	\$27,551.23	511.52	5			\$236.92	\$133.47	-\$103.46
\$757.53			6		\$25,280.39	25000.02	833.33	6		\$27,219.32	\$27,060.37	511.52	6			\$280.37	\$158.94	-\$121.43
\$758.79			7		\$24,489.20	24166.69	833.33	7		\$26,753.16	\$26,569.15	511.52	7			\$322.51	\$184.01	-\$138.49
\$760.06			8		\$23,696.68	23333.36	833.33	8		\$26,286.23	\$26,077.56	511.52	8			\$363.32	\$208.68	-\$154.65
\$761.33			9		\$22,902.85	22500.03	833.33	9		\$25,818.52	\$25,585.59	511.52	9			\$402.82	\$232.93	-\$169.89
\$762.59			10		\$22,107.69	21666.7	833.33	10		\$25,350.03	\$25,093.26	511.52	10			\$440.99	\$256.77	-\$184.22
\$763.87			11		\$21,311.20	20833.37	833.33	11		\$24,880.76	\$24,600.56	511.52	11			\$477.83	\$280.20	-\$197.64
\$765.14			12		\$20,513.39	20000.04	833.33	12		\$24,410.71	\$24,107.49	511.52	12			\$513.35	\$303.22	-\$210.14
\$766.41			13		\$19,714.25	19166.71	833.33	13		\$23,939.87	\$23,614.05	511.52	13			\$547.54	\$325.82	-\$221.72
\$767.69			14		\$18,913.78	18333.38	833.33	14		\$23,468.25	\$23,120.24	511.52	14			\$580.40	\$348.01	-\$232.39
\$768.97			15		\$18,111.97	17500.05	833.33	15		\$22,995.85	\$22,626.06	511.52	15			\$611.92	\$369.78	-\$242.14
\$770.25			16		\$17,308.83	16666.72	833.33	16		\$22,522.65	\$22,131.51	511.52	16			\$642.11	\$391.14	-\$250.97
\$771.54			17		\$16,504.35	15833.39	833.33	17		\$22,048.67	\$21,636.59	511.52	17			\$670.96	\$412.08	-\$258.88
\$772.82			18		\$15,698.52	15000.06	833.33	18		\$21,573.90	\$21,141.30	511.52	18			\$698.46	\$432.60	-\$265.86
\$774.11			19		\$14,891.36	14166.73	833.33	19		\$21,098.34	\$20,645.64	511.52	19			\$724.63	\$452.70	-\$271.93
\$775.40			20		\$14,082.85	13333.4	833.33	20		\$20,621.98	\$20,149.60	511.52	20			\$749.45	\$472.38	-\$277.07
\$776.69			21		\$13,272.99	12500.07	833.33	21		\$20,144.83	\$19,653.19	511.52	21			\$772.92	\$491.64	-\$281.28
\$777.99			22		\$12,461.78	11666.74	833.33	22		\$19,666.88	\$19,156.41	511.52	22			\$795.04	\$510.47	-\$284.57
\$779.28			23		\$11,649.22	10833.41	833.33	23		\$19,188.14	\$18,659.26	511.52	23			\$815.81	\$528.88	-\$286.93
\$780.58			24		\$10,835.31	10000.08	833.33	24		\$18,708.60	\$18,161.73	511.52	24			\$835.23	\$546.87	-\$288.36
\$781.88			25		\$10,020.03	9166.75	833.33	25		\$18,228.26	\$17,663.84	511.52	25			\$853.28	\$564.43	-\$288.86
\$783.19			26		\$9,203.40	8333.42	833.33	26		\$17,747.12	\$17,165.56	511.52	26			\$869.98	\$581.56	-\$288.42
\$784.49			27		\$8,385.41	7500.09	833.33	27		\$17,265.18	\$16,666.92	511.52	27			\$885.32	\$598.27	-\$287.06
\$785.80			28		\$7,566.06	6666.76	833.33	28		\$16,782.44	\$16,167.90	511.52	28			\$899.30	\$614.54	-\$284.76
\$787.11			29		\$6,745.34	5833.43	833.33	29		\$16,298.89	\$15,668.50	511.52	29			\$911.91	\$630.39	-\$281.52
\$788.42			30		\$5,923.25	5000.1	833.33	30		\$15,814.53	\$15,168.73	511.52	30			\$923.15	\$645.80	-\$277.35
\$789.73			31		\$5,099.79	4166.77	833.33	31		\$15,329.37	\$14,668.59	511.52	31			\$933.02	\$660.78	-\$272.24
\$791.05			32		\$4,274.96	3333.44	833.33	32		\$14,843.40	\$14,168.07	511.52	32			\$941.52	\$675.33	-\$266.20
\$792.37			33		\$3,448.76	2500.11	833.33	33		\$14,356.62	\$13,667.18	511.52	33			\$948.65	\$689.44	-\$259.21
\$793.69			34		\$2,621.18	1666.78	833.33	34		\$13,869.03	\$13,165.91	511.52	34			\$954.40	\$703.12	-\$251.28
\$795.01			35		\$1,792.21	833.45	833.33	35		\$13,380.62	\$12,664.26	511.52	35			\$958.76	\$716.36	-\$242.41
\$796.34			36		\$961.87	0.12		36		\$12,891.40	\$12,162.24	511.52	36			\$961.75	\$729.16	-\$232.59
\$797.66			37		\$963.47			37		\$12,401.37	\$11,659.84	511.52	37			\$963.47	\$741.53	-\$221.95
\$798.99			38		\$965.08			38		\$11,910.52	\$11,157.07	511.52	38			\$965.08	\$753.45	-\$211.63
\$800.33			39		\$966.69			39		\$11,418.85	\$10,653.92	511.52	39			\$966.69	\$764.93	-\$201.76
\$801.66			40		\$968.30			40		\$10,926.36	\$10,150.39	511.52	40			\$968.30	\$775.97	-\$192.33
\$803.00			41		\$969.91			41		\$10,433.05	\$9,646.48	511.52	41			\$969.91	\$786.57	-\$183.34
\$804.33			42		\$971.53			42		\$9,938.92	\$9,142.19	511.52	42			\$971.53	\$796.72	-\$174.81
\$805.67			43		\$973.15			43		\$9,443.96	\$8,637.53	511.52	43			\$973.15	\$806.43	-\$166.72
\$807.02			44		\$974.77			44		\$8,948.18	\$8,132.49	511.52	44			\$974.77	\$815.69	-\$159.08
\$808.36			45		\$976.40			45		\$8,451.58	\$7,627.07	511.52	45			\$976.40	\$824.51	-\$151.89
\$809.71			46		\$978.02			46		\$7,954.14	\$7,121.27	511.52	46			\$978.02	\$832.87	-\$145.15
\$811.06			47		\$979.65			47		\$7,455.88	\$6,615.09	511.52	47			\$979.65	\$840.79	-\$138.86
\$812.41			48		\$981.29			48		\$6,956.79	\$6,108.53	511.52	48			\$981.29	\$848.26	-\$133.03
\$813.77			49		\$982.92			49		\$6,456.86	\$5,601.59	511.52	49			\$982.92	\$855.27	-\$127.65
\$815.12			50		\$984.56			50		\$5,956.10	\$5,094.27	511.52	50			\$984.56	\$861.83	-\$122.73
\$816.48			51		\$986.20			51		\$5,454.51	\$4,586.57	511.52	51			\$986.20	\$867.94	-\$118.27
\$817.84			52		\$987.84			52		\$4,952.08	\$4,078.49	511.52	52			\$987.84	\$873.59	-\$114.26
\$819.20			53		\$989.49			53		\$4,448.81	\$3,570.03	511.52	53			\$989.49	\$878.78	-\$110.71
\$820.57			54		\$991.14			54		\$3,944.71	\$3,061.19	511.52	54			\$991.14	\$883.52	-\$107.62
\$821.94			55		\$992.79			55		\$3,439.76	\$2,551.97	511.52	55			\$992.79	\$887.80	-\$105.00
\$823.31			56		\$994.45			56		\$2,933.98	\$2,042.36	511.52	56			\$994.45	\$891.62	-\$102.83
\$824.68			57		\$996.10			57		\$2,427.35	\$1,532.37	511.52	57			\$996.10	\$894.97	-\$101.13
\$826.05			58		\$997.76			58		\$1,919.87	\$1,022.00	511.52	58			\$997.76	\$897.87	-\$99.89
\$827.43			59		\$999.43			59		\$1,411.55	\$511.25	511.52	59			\$999.43	\$900.30	-\$99.12
\$828.81			60		\$1,001.09			60		\$902.38	\$0.11	511.52	60			\$1,001.09	\$902.27	-\$98.82
``````

Code: Select all

``````Savings	Loan	Payment	Month		Savings	Loan	Payment	Month		Savings	Loan	Payment	Month
\$750.00	0		0		\$30,000.00	30000	833.33	0		\$30,000.00	30000	511.52	0			\$0.00	\$0.00	\$0.00
\$753.13			1		\$29,291.67	29166.67	833.33	1		\$29,613.48	\$29,510.98	511.52	1			\$125.00	\$102.50	-\$22.50
\$756.26			2		\$28,580.39	28333.34	833.33	2		\$29,225.35	\$29,021.59	511.52	2			\$247.05	\$203.76	-\$43.29
\$759.41			3		\$27,866.14	27500.01	833.33	3		\$28,835.60	\$28,531.84	511.52	3			\$366.13	\$303.76	-\$62.37
\$762.58			4		\$27,148.92	26666.68	833.33	4		\$28,444.23	\$28,041.72	511.52	4			\$482.24	\$402.51	-\$79.73
\$765.76			5		\$26,428.71	25833.35	833.33	5		\$28,051.23	\$27,551.23	511.52	5			\$595.36	\$500.00	-\$95.36
\$768.95			6		\$25,705.50	25000.02	833.33	6		\$27,656.59	\$27,060.37	511.52	6			\$705.48	\$596.21	-\$109.27
\$772.15			7		\$24,979.28	24166.69	833.33	7		\$27,260.30	\$26,569.15	511.52	7			\$812.59	\$691.16	-\$121.43
\$775.37			8		\$24,250.03	23333.36	833.33	8		\$26,862.37	\$26,077.56	511.52	8			\$916.67	\$784.81	-\$131.86
\$778.60			9		\$23,517.74	22500.03	833.33	9		\$26,462.77	\$25,585.59	511.52	9			\$1,017.71	\$877.18	-\$140.53
\$781.84			10		\$22,782.40	21666.7	833.33	10		\$26,061.52	\$25,093.26	511.52	10			\$1,115.70	\$968.25	-\$147.45
\$785.10			11		\$22,044.00	20833.37	833.33	11		\$25,658.59	\$24,600.56	511.52	11			\$1,210.63	\$1,058.02	-\$152.60
\$788.37			12		\$21,302.52	20000.04	833.33	12		\$25,253.98	\$24,107.49	511.52	12			\$1,302.48	\$1,146.48	-\$155.99
\$791.66			13		\$20,557.95	19166.71	833.33	13		\$24,847.68	\$23,614.05	511.52	13			\$1,391.24	\$1,233.63	-\$157.61
\$794.95			14		\$19,810.28	18333.38	833.33	14		\$24,439.69	\$23,120.24	511.52	14			\$1,476.90	\$1,319.45	-\$157.45
\$798.27			15		\$19,059.49	17500.05	833.33	15		\$24,030.01	\$22,626.06	511.52	15			\$1,559.44	\$1,403.94	-\$155.50
\$801.59			16		\$18,305.57	16666.72	833.33	16		\$23,618.61	\$22,131.51	511.52	16			\$1,638.85	\$1,487.10	-\$151.76
\$804.93			17		\$17,548.52	15833.39	833.33	17		\$23,205.50	\$21,636.59	511.52	17			\$1,715.13	\$1,568.91	-\$146.22
\$808.29			18		\$16,788.31	15000.06	833.33	18		\$22,790.67	\$21,141.30	511.52	18			\$1,788.25	\$1,649.37	-\$138.87
\$811.66			19		\$16,024.93	14166.73	833.33	19		\$22,374.11	\$20,645.64	511.52	19			\$1,858.20	\$1,728.48	-\$129.72
\$815.04			20		\$15,258.37	13333.4	833.33	20		\$21,955.82	\$20,149.60	511.52	20			\$1,924.97	\$1,806.22	-\$118.75
\$818.43			21		\$14,488.61	12500.07	833.33	21		\$21,535.78	\$19,653.19	511.52	21			\$1,988.54	\$1,882.59	-\$105.96
\$821.84			22		\$13,715.65	11666.74	833.33	22		\$21,113.99	\$19,156.41	511.52	22			\$2,048.91	\$1,957.58	-\$91.33
\$825.27			23		\$12,939.47	10833.41	833.33	23		\$20,690.45	\$18,659.26	511.52	23			\$2,106.06	\$2,031.19	-\$74.87
\$828.71			24		\$12,160.06	10000.08	833.33	24		\$20,265.14	\$18,161.73	511.52	24			\$2,159.98	\$2,103.40	-\$56.57
\$832.16			25		\$11,377.39	9166.75	833.33	25		\$19,838.06	\$17,663.84	511.52	25			\$2,210.64	\$2,174.22	-\$36.42
\$835.63			26		\$10,591.47	8333.42	833.33	26		\$19,409.19	\$17,165.56	511.52	26			\$2,258.05	\$2,243.63	-\$14.42
\$839.11			27		\$9,802.27	7500.09	833.33	27		\$18,978.55	\$16,666.92	511.52	27			\$2,302.18	\$2,311.63	\$9.45
\$842.60			28		\$9,009.78	6666.76	833.33	28		\$18,546.10	\$16,167.90	511.52	28			\$2,343.02	\$2,378.21	\$35.18
\$846.12			29		\$8,213.99	5833.43	833.33	29		\$18,111.86	\$15,668.50	511.52	29			\$2,380.56	\$2,443.36	\$62.79
\$849.64			30		\$7,414.89	5000.1	833.33	30		\$17,675.81	\$15,168.73	511.52	30			\$2,414.79	\$2,507.07	\$92.28
\$853.18			31		\$6,612.45	4166.77	833.33	31		\$17,237.93	\$14,668.59	511.52	31			\$2,445.68	\$2,569.34	\$123.66
\$856.74			32		\$5,806.68	3333.44	833.33	32		\$16,798.24	\$14,168.07	511.52	32			\$2,473.24	\$2,630.17	\$156.93
\$860.31			33		\$4,997.54	2500.11	833.33	33		\$16,356.71	\$13,667.18	511.52	33			\$2,497.43	\$2,689.53	\$192.10
\$863.89			34		\$4,185.03	1666.78	833.33	34		\$15,913.34	\$13,165.91	511.52	34			\$2,518.25	\$2,747.44	\$229.18
\$867.49			35		\$3,369.14	833.45	833.33	35		\$15,468.13	\$12,664.26	511.52	35			\$2,535.69	\$2,803.87	\$268.17
\$871.10			36		\$2,549.85	0.12		36		\$15,021.06	\$12,162.24	511.52	36			\$2,549.73	\$2,858.82	\$309.09
\$874.73			37		\$2,560.47			37		\$14,572.13	\$11,659.84	511.52	37			\$2,560.47	\$2,912.29	\$351.81
\$878.38			38		\$2,571.14			38		\$14,121.33	\$11,157.07	511.52	38			\$2,571.14	\$2,964.26	\$393.11
\$882.04			39		\$2,581.86			39		\$13,668.64	\$10,653.92	511.52	39			\$2,581.86	\$3,014.73	\$432.87
\$885.71			40		\$2,592.61			40		\$13,214.08	\$10,150.39	511.52	40			\$2,592.61	\$3,063.69	\$471.08
\$889.40			41		\$2,603.42			41		\$12,757.62	\$9,646.48	511.52	41			\$2,603.42	\$3,111.14	\$507.72
\$893.11			42		\$2,614.26			42		\$12,299.25	\$9,142.19	511.52	42			\$2,614.26	\$3,157.06	\$542.79
\$896.83			43		\$2,625.16			43		\$11,838.98	\$8,637.53	511.52	43			\$2,625.16	\$3,201.45	\$576.29
\$900.57			44		\$2,636.09			44		\$11,376.79	\$8,132.49	511.52	44			\$2,636.09	\$3,244.30	\$608.20
\$904.32			45		\$2,647.08			45		\$10,912.67	\$7,627.07	511.52	45			\$2,647.08	\$3,285.60	\$638.53
\$908.09			46		\$2,658.11			46		\$10,446.62	\$7,121.27	511.52	46			\$2,658.11	\$3,325.35	\$667.24
\$911.87			47		\$2,669.18			47		\$9,978.63	\$6,615.09	511.52	47			\$2,669.18	\$3,363.54	\$694.36
\$915.67			48		\$2,680.31			48		\$9,508.69	\$6,108.53	511.52	48			\$2,680.31	\$3,400.16	\$719.85
\$919.49			49		\$2,691.47			49		\$9,036.79	\$5,601.59	511.52	49			\$2,691.47	\$3,435.19	\$743.72
\$923.32			50		\$2,702.69			50		\$8,562.92	\$5,094.27	511.52	50			\$2,702.69	\$3,468.65	\$765.96
\$927.17			51		\$2,713.95			51		\$8,087.08	\$4,586.57	511.52	51			\$2,713.95	\$3,500.50	\$786.56
\$931.03			52		\$2,725.26			52		\$7,609.25	\$4,078.49	511.52	52			\$2,725.26	\$3,530.76	\$805.50
\$934.91			53		\$2,736.61			53		\$7,129.44	\$3,570.03	511.52	53			\$2,736.61	\$3,559.41	\$822.79
\$938.80			54		\$2,748.01			54		\$6,647.63	\$3,061.19	511.52	54			\$2,748.01	\$3,586.43	\$838.42
\$942.71			55		\$2,759.46			55		\$6,163.80	\$2,551.97	511.52	55			\$2,759.46	\$3,611.84	\$852.37
\$946.64			56		\$2,770.96			56		\$5,677.97	\$2,042.36	511.52	56			\$2,770.96	\$3,635.61	\$864.64
\$950.59			57		\$2,782.51			57		\$5,190.10	\$1,532.37	511.52	57			\$2,782.51	\$3,657.73	\$875.22
\$954.55			58		\$2,794.10			58		\$4,700.21	\$1,022.00	511.52	58			\$2,794.10	\$3,678.21	\$884.11
\$958.53			59		\$2,805.74			59		\$4,208.27	\$511.25	511.52	59			\$2,805.74	\$3,697.03	\$891.28
\$962.52			60		\$2,817.43			60		\$3,714.29	\$0.11	511.52	60			\$2,817.43	\$3,714.18	\$896.74
``````

White Coat Investor
Posts: 13443
Joined: Fri Mar 02, 2007 9:11 pm
Location: Greatest Snow On Earth

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

markcoop wrote:
Wed Mar 21, 2018 1:50 pm
Deciding between these 3 payment options to buy new car:
1) Pay full amount - get \$750 discount
2) 0% 36 months - no discount
3) 0.9% 60 months - no discount

Assuming I can afford either option, which do you think is best?

I believe the answer lies in what interest rate I can get for the money I am holding. In case 1, I earn a small amount of interest on the \$750 saved. In case 2, it's just the balance of the loan times the interest rate for each period. In case 3, it's the balance of the loan times the interest rate for each period minus the interest paid. Plugging in some numbers into a spread sheet, at a low interest rate (roughly below 1.5%) option 1 is best, at a middle interest rate (around 2%) option 2 is best and at a higher interest rate (roughly above 2.5%) option 3 is best.

Opinions?
How long do you want to be in debt for? I'm not interested in going back into debt, so I'd choose option 1, especially with a discount. No brainer for me.

But yes, the mathematically optimal thing is usually to maximally leverage your life whenever possible.
1) Invest you must 2) Time is your friend 3) Impulse is your enemy | 4) Basic arithmetic works 5) Stick to simplicity 6) Stay the course

Tamarind
Posts: 1148
Joined: Mon Nov 02, 2015 2:38 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

If it's an apples to apples comparison, pay in full.

If your credit score is strong enough to get those rates, you should expect to be offered some kind of sweetener to take the financing. Usually this comes in the form of a reduction in price with requirement to keep the loan for some period of time.

TheOscarGuy
Posts: 549
Joined: Sat Oct 06, 2012 1:10 pm
Location: Where I wanna be.

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

markcoop wrote:
Wed Mar 21, 2018 1:50 pm
Deciding between these 3 payment options to buy new car:
1) Pay full amount - get \$750 discount
2) 0% 36 months - no discount
3) 0.9% 60 months - no discount

Assuming I can afford either option, which do you think is best?

I believe the answer lies in what interest rate I can get for the money I am holding. In case 1, I earn a small amount of interest on the \$750 saved. In case 2, it's just the balance of the loan times the interest rate for each period. In case 3, it's the balance of the loan times the interest rate for each period minus the interest paid. Plugging in some numbers into a spread sheet, at a low interest rate (roughly below 1.5%) option 1 is best, at a middle interest rate (around 2%) option 2 is best and at a higher interest rate (roughly above 2.5%) option 3 is best.

Opinions?
If you can afford it, but it in cash.
For a period of 5 years or earlier, I can not justify monies be invested -- which means your options are limited, as you stated in your spreadsheet analysis, I think. At this low numbers, its really trivial difference.
For me, pay full amount and get full peace of mind of owing a car fair and square.

livesoft
Posts: 62719
Joined: Thu Mar 01, 2007 8:00 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Don't forget to factor in inflation over the term of the loan. You will be repaying with dollars that may have lost value.

Back of envelope calculation: 3-year loan of \$30K will have an average balance outstanding of \$15K which can easily earn 1.5% each year. That's \$225 a year or \$675 total less any taxes. The \$750 discount is like being paid about \$250 a year or a simple rate of 1.67% on \$15K, so any bump in interest earned on investing gives you a win.

Of course, you could invest the \$30K on an RBD and very likely make more than 1.5% in a few days.

I took the 0% loan a few years ago and made whatever the stock market gave me over the past 3 years.

Now people will complain: But you didn't invest risk-free which is what paying cash gives you. Sure, I took the risk that I would not sell if I lost money in the stock market, but would wait until I made money. That is, I had no need to sell at a loss except for tax-loss harvesting purposes. I could practically guarantee that the stock market would not be lower every single day over the 3 years of my loan.
This signature message sponsored by sscritic: Learn to fish.

2m2037
Posts: 203
Joined: Mon May 08, 2017 4:48 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

I would pay in full just so that I don't have to deal with the administrative costs of making regular payments (for example, if you close the bank account you use for automatic payments).

The opportunity cost, if any, is likely to be immaterial.

JBTX
Posts: 4045
Joined: Wed Jul 26, 2017 12:46 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

The 36 month loans comes out to approx 0.8% interest per year

The 60 month loan is approx .9+0.5= 1.4% per year.

You could probably easily find a 5 year cd at 1.4%.

Clever_Username
Posts: 1046
Joined: Sun Jul 15, 2012 12:24 am
Location: Southern California

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Assuming the insurance requirements are the same, I would go with a loan. I would do this *after* determining what the (pre-interest, in event of option 3) cost is. If I had to buy a new car tomorrow, I could write a check for the one I want (well, I'd need to order a checkbook, but other than that).

Here's why I'd go with a loan: I already have a significantly positive cash flow every month, so swinging a car payment isn't an issue. And if you gave me the option to borrow a good sum of money at 0% for 36 months, requiring regular payments, I'd take it in a heartbeat. And at 0.9% for 60 months, also requiring payments, I'd do that too.

If the option came up tomorrow, I'd keep the car purchase price in my taxable bond fund (as it already is), order the checkbook, and write a check from that account each month for the car payments.
"What was true then is true now. Have a plan. Stick to it." -- XXXX, _Layer Cake_

Toons
Posts: 12970
Joined: Fri Nov 21, 2008 10:20 am
Location: Hills of Tennessee

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

1) Pay full amount - get \$750 discount

Bingo.
Do That.
Then forget about it.
Let Go Of The Mental Baggage
Move On.

Last edited by Toons on Wed Mar 21, 2018 6:11 pm, edited 1 time in total.
"One does not accumulate but eliminate. It is not daily increase but daily decrease. The height of cultivation always runs to simplicity" –Bruce Lee

mortfree
Posts: 1280
Joined: Mon Sep 12, 2016 7:06 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

If you get a loan you can put down 5k or 10k or any other amount.

It’s somewhere in between the three ideas you listed.

I’m surprised you’re getting a discount for cash. I’ve read several situations where the person was going to pay cash but the dealership gave them a lower price to finance through them. YMMV in those cases

markcoop
Posts: 796
Joined: Fri Mar 02, 2007 8:36 am

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Thanks all. I think there were a number of interesting responses. I posed the question taking nothing else into account (the best way to initially work on a problem), but of course, as one poster mentioned, you have to take everything into consideration.

Some comments:
1) I don't think the correct comparison is to find a 5-year investment because I need to keep making payments. maybe you could divide into 4ths (keep one years worth liquid) and buy 1 yr, 2yr, 3 yr, 4yr cds.

2) My view is to view it as a short term goal and should be invested conservatively. In reality, I'm much more likely to just take it out of my one big pot of money, so the rate would be my AA.

3) One piece I didn't mention here was my cash flow. Pay in full is possible, but would be alot easier for my cash flow to do one of the loans.

4) My initial gut was to do to the 3-year loan and at this point that is the way I am still leaning.

I do believe I would be fine with any of these options, but I am never one to shy away from a good math-related problem. In fact, I thought it was a great question to share with my kids.
Mark

misterno
Posts: 478
Joined: Sat Mar 08, 2014 7:55 am

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

markcoop wrote:
Wed Mar 21, 2018 1:50 pm
Deciding between these 3 payment options to buy new car:
1) Pay full amount - get \$750 discount
2) 0% 36 months - no discount
3) 0.9% 60 months - no discount

Assuming I can afford either option, which do you think is best?

I believe the answer lies in what interest rate I can get for the money I am holding. In case 1, I earn a small amount of interest on the \$750 saved. In case 2, it's just the balance of the loan times the interest rate for each period. In case 3, it's the balance of the loan times the interest rate for each period minus the interest paid. Plugging in some numbers into a spread sheet, at a low interest rate (roughly below 1.5%) option 1 is best, at a middle interest rate (around 2%) option 2 is best and at a higher interest rate (roughly above 2.5%) option 3 is best.

Opinions?
I would pay full and save from interest and then get liability only insurance save from there also

but this is me. I am a cheap skate

Say I am in a very good mood and my wife smiles all day long, then I can go with the 5 yr option with 0.9% interest.

Cramerica
Posts: 226
Joined: Sat Oct 03, 2015 5:30 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

When these auto loan percentages are quoted, are they simple or compound interest?

I would pick 3 here myself.

It seems like some people are picking 2 by mixing the psychology of having a "0%" loan with the math advantage of leverage?

Otherwise, it seems that option 3 would clearly win given the decreased risk in equities with a longer holding period and the longer compounding period. What am I missing?

staythecourse
Posts: 6017
Joined: Mon Jan 03, 2011 9:40 am

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

markcoop wrote:
Wed Mar 21, 2018 1:50 pm
Deciding between these 3 payment options to buy new car:
1) Pay full amount - get \$750 discount
2) 0% 36 months - no discount
3) 0.9% 60 months - no discount

Assuming I can afford either option, which do you think is best?

I believe the answer lies in what interest rate I can get for the money I am holding. In case 1, I earn a small amount of interest on the \$750 saved. In case 2, it's just the balance of the loan times the interest rate for each period. In case 3, it's the balance of the loan times the interest rate for each period minus the interest paid. Plugging in some numbers into a spread sheet, at a low interest rate (roughly below 1.5%) option 1 is best, at a middle interest rate (around 2%) option 2 is best and at a higher interest rate (roughly above 2.5%) option 3 is best.

Opinions?
I'm totally biased and UNbogleheads in this type of situation. I EASILY choose low interest rate debt and would take the money and just throw it into my asset allocation.

Good luck.
"The stock market [fluctuation], therefore, is noise. A giant distraction from the business of investing.” | -Jack Bogle

Nate79
Posts: 3503
Joined: Thu Aug 11, 2016 6:24 pm
Location: Portland, OR

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Pay in cash as long as you have a healthy emergency fund. The difference is picking pennies up off the ground. If this has any material affect on your future you likely can't afford the car in the first place.

Nate79
Posts: 3503
Joined: Thu Aug 11, 2016 6:24 pm
Location: Portland, OR

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Double post

Nestegg_User
Posts: 1034
Joined: Wed Aug 05, 2009 1:26 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

mortfree wrote:
Wed Mar 21, 2018 6:11 pm
If you get a loan you can put down 5k or 10k or any other amount.

It’s somewhere in between the three ideas you listed.

I’m surprised you’re getting a discount for cash. I’ve read several situations where the person was going to pay cash but the dealership gave them a lower price to finance through them. YMMV in those cases
Yep... I was a responder

choice after best price.... pay cash, no discount
or take financing and get \$1250 off, paid two months of interest (total of \$85) then paid it off....WIN

given the choices ... I’d go with three years at zero... and put into CD ladder as two year are over 2%, so 18 month and two year CD with rest in regular deposit account for cash flow. You can decide how much to put down vs finance to best match your cash flow needs.

Agggm
Posts: 227
Joined: Mon Dec 25, 2017 6:18 pm

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

markcoop wrote:
Wed Mar 21, 2018 1:50 pm
Deciding between these 3 payment options to buy new car:
1) Pay full amount - get \$750 discount
2) 0% 36 months - no discount
3) 0.9% 60 months - no discount

Assuming I can afford either option, which do you think is best?

I believe the answer lies in what interest rate I can get for the money I am holding. In case 1, I earn a small amount of interest on the \$750 saved. In case 2, it's just the balance of the loan times the interest rate for each period. In case 3, it's the balance of the loan times the interest rate for each period minus the interest paid. Plugging in some numbers into a spread sheet, at a low interest rate (roughly below 1.5%) option 1 is best, at a middle interest rate (around 2%) option 2 is best and at a higher interest rate (roughly above 2.5%) option 3 is best.

Opinions?
Unless you're buying a high end car with high relative demand, 750 discount is weak. None of these options are appealing.

markcoop
Posts: 796
Joined: Fri Mar 02, 2007 8:36 am

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Agggm wrote:
Wed Mar 21, 2018 8:24 pm
markcoop wrote:
Wed Mar 21, 2018 1:50 pm
Deciding between these 3 payment options to buy new car:
1) Pay full amount - get \$750 discount
2) 0% 36 months - no discount
3) 0.9% 60 months - no discount

Assuming I can afford either option, which do you think is best?

I believe the answer lies in what interest rate I can get for the money I am holding. In case 1, I earn a small amount of interest on the \$750 saved. In case 2, it's just the balance of the loan times the interest rate for each period. In case 3, it's the balance of the loan times the interest rate for each period minus the interest paid. Plugging in some numbers into a spread sheet, at a low interest rate (roughly below 1.5%) option 1 is best, at a middle interest rate (around 2%) option 2 is best and at a higher interest rate (roughly above 2.5%) option 3 is best.

Opinions?
Unless you're buying a high end car with high relative demand, 750 discount is weak. None of these options are appealing.
I wasn't being totally honest in my description. Case (1) was actually save \$1,450. Cases (2) and (3) were save \$700. So, in all cases, I am going to save \$700, so I took that out of the equation not to muddy the decision making process.
Mark

flamesabers
Posts: 1743
Joined: Fri Mar 03, 2017 12:05 pm
Location: Rochester, MN

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

markcoop wrote:
Thu Mar 22, 2018 8:57 am
Case (1) was actually save \$1,450. Cases (2) and (3) were save \$700. So, in all cases, I am going to save \$700, so I took that out of the equation not to muddy the decision making process.
My suggestion would be to pay in full. The savings for option #1 is immediate, guaranteed and tax-free. Nobody knows for certain what interest rates will be for the next 3-5 years.

randomguy
Posts: 6302
Joined: Wed Sep 17, 2014 9:00 am

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

mortfree wrote:
Wed Mar 21, 2018 6:11 pm
If you get a loan you can put down 5k or 10k or any other amount.

It’s somewhere in between the three ideas you listed.

I’m surprised you’re getting a discount for cash. I’ve read several situations where the person was going to pay cash but the dealership gave them a lower price to finance through them. YMMV in those cases
A lot of the time the deal is you can get x bonus cash or a subsidies rate. This probably an OEM discount not a dealer one.

djpeteski
Posts: 634
Joined: Fri Mar 31, 2017 9:07 am

### Re: Math question to buy new car: pay full, 0% 36 months, 0.9% 60 months

Option 1 is the best.