Interest Rate Calculation

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MrDogg
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Interest Rate Calculation

Postby MrDogg » Tue Jan 10, 2017 5:15 pm

Can someone help me calculate my net interest rate for the following circumstance?

I am loaning $50K for 60 months at a simple interest rate of 5.25%, the monthly payment to me will be $949.30 (loan is highly secured). I am going to deposit each monthly payment as it is received into an account that pays 2.5% simple interest. Assuming the loan repayment and account deposits run the full 60 month term, what is the actual interest rate I will be receiving?

Thanks in advance to any of you math wizards that can provide the answer.

harikaried
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Re: Interest Rate Calculation

Postby harikaried » Tue Jan 10, 2017 5:45 pm

Looks like $60,561 after 60 months if I put things right into Wolfram Alpha:

$949.30/mo compounded at 2.5% APR, 60 months
http://www.wolframalpha.com/input/?i=$9 ... +60+months

PV=$50k, FV=$60561, 5 years
http://www.wolframalpha.com/input/?i=PV ... 1,+5+years

Results in 3.839%

alex_686
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Re: Interest Rate Calculation

Postby alex_686 » Tue Jan 10, 2017 5:57 pm

harikaried wrote:Results in 3.839%


Harikaried, I think you calculations are a bit off. You are not assuming monthly deposits and you are assuming compounding interest.

Which leads me to my next questions, MrDogg: Why no compounding interest on the savings side? Except for loans with negative amortization, loans always are simple interest. On the flip side, I don't know of any savings account that does not compound interest. It seems like very odd parameters.

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dm200
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Re: Interest Rate Calculation

Postby dm200 » Tue Jan 10, 2017 6:15 pm

I believe a good approximation (because this is only 60 months and the loan interest rate is not that high) is to assume that (on average) over the five years half received 5.25 and half receives 2.50. That is 3.875%. There will, in actuality, be a few more months where the loan is more than half, so a bit above the 3.875%.

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dm200
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Re: Interest Rate Calculation

Postby dm200 » Tue Jan 10, 2017 6:18 pm

Except for loans with negative amortization, loans always are simple interest.


1. I do not think "always" is correct.

2. While perhaps "simple interest" most mortgage loans collect a full month's interest even if paid early. Such loan calculations yield different results than a loan where interest is based on the actual principal outtanding for the number of days.

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Kevin M
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Re: Interest Rate Calculation

Postby Kevin M » Tue Jan 10, 2017 6:23 pm

Agreed that an average of the two rates is a decent approximation.

For 949.30 at 2.5%/12 compounded monthly for 60 months I get FV of 60,604. With a PV of 50,000, I get an annual rate of 3.92%. Pretty close to the approximation of 3.88%.

Kevin
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MrDogg
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Re: Interest Rate Calculation

Postby MrDogg » Wed Jan 11, 2017 8:15 am

alex_686 wrote:
harikaried wrote:Results in 3.839%



Why no compounding interest on the savings side? Except for loans with negative amortization, loans always are simple interest. On the flip side, I don't know of any savings account that does not compound interest. It seems like very odd parameters.


To clarify: You are correct, it will be compounded interest on the savings deposit side.

MrDogg
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Re: Interest Rate Calculation

Postby MrDogg » Wed Jan 11, 2017 8:22 am

Thanks to all who responded. For my purposes the average of the two rates is close enough as it approximates all the other methods presented. Thanks again everyone.

alex_686
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Re: Interest Rate Calculation

Postby alex_686 » Wed Jan 11, 2017 11:11 am

dm200 wrote:
Except for loans with negative amortization, loans always are simple interest.


1. I do not think "always" is correct.

2. While perhaps "simple interest" most mortgage loans collect a full month's interest even if paid early. Such loan calculations yield different results than a loan where interest is based on the actual principal outtanding for the number of days.


I would be interested in a real life example if you could find one. The mortgage interest example does not exactly fit. Compound interest is interest on interest. In the mortgage example the issue is that the banks only book the payments to the loan once a month. A analogy would be making a loan payment on a Saturday. While the journal entry might have the Saturday date it would not be applied until Monday.

alex_686
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Re: Interest Rate Calculation

Postby alex_686 » Wed Jan 11, 2017 11:17 am

MrDogg wrote:Thanks to all who responded. For my purposes the average of the two rates is close enough as it approximates all the other methods presented. Thanks again everyone.


I don't think you want the average, I think you want the spread. 5.25% - 2.5% = 1.75%. i.e., This project will allow you to pick up an extra 1.75% return for this risk you take. If you want to be really precise what you will want to do is a Internal Rate of Return. You will want to model every cash flow in and out. You will need a spreadsheet to calculate this.

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dm200
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Re: Interest Rate Calculation

Postby dm200 » Wed Jan 11, 2017 11:40 am

alex_686 wrote:
dm200 wrote:
Except for loans with negative amortization, loans always are simple interest.

1. I do not think "always" is correct.
2. While perhaps "simple interest" most mortgage loans collect a full month's interest even if paid early. Such loan calculations yield different results than a loan where interest is based on the actual principal outtanding for the number of days.

I would be interested in a real life example if you could find one. The mortgage interest example does not exactly fit. Compound interest is interest on interest. In the mortgage example the issue is that the banks only book the payments to the loan once a month. A analogy would be making a loan payment on a Saturday. While the journal entry might have the Saturday date it would not be applied until Monday.


I would regard loans with sgnificant prepayment penalties as not "simple interest". If reasonable, though, I would not regard them as "unfair", though. Such "prepayment penalties" are not uncommon. I would also not regard loans with a large amount of fees and charges (inclusing those classified as prepaid interest) as pure "simple interest" loans.

I don't know if they still exist, but loans where the interest is calcuated up front, then when/if paid early the refunds is based on the "rule of 78s" are certainly not simple interest.

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Kevin M
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Re: Interest Rate Calculation

Postby Kevin M » Wed Jan 11, 2017 1:18 pm

alex_686 wrote:
MrDogg wrote:Thanks to all who responded. For my purposes the average of the two rates is close enough as it approximates all the other methods presented. Thanks again everyone.

I don't think you want the average, I think you want the spread. 5.25% - 2.5% = 1.75%. i.e., This project will allow you to pick up an extra 1.75% return for this risk you take. If you want to be really precise what you will want to do is a Internal Rate of Return. You will want to model every cash flow in and out. You will need a spreadsheet to calculate this.

I thought about taking an IRR approach. However, you can think of the loan plus savings account as a single entity in the cash flow analysis, which allows you to reduce the analysis to a single cash flow in of $50K and a single cash flow out of the final value of the savings account.

This is similar to reinvesting dividends or interest. You could count each reinvestment as a cash flow out and cash flow in, but since they are equal magnitude but opposite sign, they cancel each other out, resulting in a net cash flow of 0, so there's no need to do the extra calculations. In this case, the cash flow out from each monthly loan payment is cancelled by the cash flow into the savings account. Net result is a single cash flow in and single cash flow out.

If you use XIRR on the two cashflows, -50,000 and +60,604 on dates 1/1/2000 and 1/1/2005 (or any two dates five years apart), you get the exact same answer as by using the PV function: 3.92%. Basically this answers the question, "If I invest 50K and five years later have 60,604, what is my annual rate of return?"

The rate of return would be higher if you received the cash flows instead of reinvesting them at 2.5%, because the earlier cashflows are discounted at a lower rate. Doing an XIRR with receiving the monthly cashflows gives a rate of 5.38%, which is the effective rate for a nominal rate of 5.25% with 12 periods per year. This is exactly what you'd earn if the savings account paid 5.25% instead of 2.5%, which can be verified by redoing the FV/PV analysis with these rates.

I don't see how you'll get any other answer with an IRR approach, but I'd certainly be interested to see it if someone thinks you can.

Kevin
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MrDogg
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Re: Interest Rate Calculation

Postby MrDogg » Wed Jan 11, 2017 3:04 pm

[/quote]
If you use XIRR on the two cashflows, -50,000 and +60,604 on dates 1/1/2000 and 1/1/2005 (or any two dates five years apart), you get the exact same answer as by using the PV function: 3.92%. Basically this answers the question, "If I invest 50K and five years later have 60,604, what is my annual rate of return?"
Kevin[/quote]

Excellent response. This puts the transaction in perspective for me. Thanks

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jimb_fromATL
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Re: Interest Rate Calculation

Postby jimb_fromATL » Wed Jan 11, 2017 3:48 pm

MrDogg wrote:Can someone help me calculate my net interest rate for the following circumstance?

I am loaning $50K for 60 months at a simple interest rate of 5.25%, the monthly payment to me will be $949.30 (loan is highly secured). I am going to deposit each monthly payment as it is received into an account that pays 2.5% simple interest. Assuming the loan repayment and account deposits run the full 60 month term, what is the actual interest rate I will be receiving?

Thanks in advance to any of you math wizards that can provide the answer.


You are receiving an income of 5.25% APY compounded monthly on your lump sum investment of $50K. And you are receiving 2.5% compounded monthly on a series of payments into another account.

The borrower's debt is the lender's investment in an annuity that has a guaranteed annual rate of return and a guaranteed minimum monthly payment, with interest compounded monthly on the unpaid balance. The math formulas are exactly the same for loans and investments. The only difference is which way the cash is flowing -- out of your pocket if you are the borrower, or into your pocket if you are the lender/investor.

Since the unpaid balance goes down every month in an amortized loan, the ratio of interest to principal changes with every payment. The fixed minimum payment is calculated so that the changing ratio will result in paying the annual rate and all the principal in the given original time.

In most fixed payment amortized loans --such as mortgages and car loans -- interest is calculated on the unpaid balance at 1/12 of the yearly rate regardless of when the payment is received.

On open ended loans like credit cards and lines of credit, and on student loans, the initial payment is calculated for compounding at 1/12 of the yearly rate the same way – which is the average rate per month. However, interest is actually calculated on a daily basis as of the time the payment is received and posted. So with varying times between actual payments, the actual time required and total interest paid may be slightly different by the end of the loan. (Typically when the payments are made on a regular basis, the last payment will merely be a little smaller or larger.)

I'm including links below to several of my posts that explain how to use the math library functions in Excel and other spreadsheets and software libraries to do the tedious iterative math for you to get the end results.

Here's how the math functions work for you:

    For an amortized loan balance of $50,000 at 5.25% for 60. months, the payment is $949.30.
    =PMT(5.25%/12,60,-50000) … returns $949.30.
    The borrower will pay a total of 60 x 949.30 = $56,958 with $50,000 principal and $6,958 interest.

    If you invest $50,000 in a lump sum and earn 5.25% compounded monthly you can withdraw a monthly annuity of $949.30 per month for 5 years before it is all gone. You will receive a total of 60 x 949.3 = $56,958 with $6,958 interest earned.
    As a double-check,
    =RATE(60,949.30,-50000)* 12 returns 5.25%

    Investing the $949.30 per month in an account earing an average APY of 2.5% compounded monthly will give you
    =FV(2.5%/12, 60, -949.30) … which returns $60,603.77.

    Since you're not actually using the monthly payment, you can solve for the equivalent rate required for a $50,000 investment to give you $60,603.77 in 60 months with either:

      =RATE(60, 0, 50000, -60603.77 ) * 12 = 3.853% compounded monthly
      or =RATE(5, 0, 50000, -60603.77) ... which returns 3.922% compounded yearly.
    Again double-checking
    =FV(3.853%/12,60,0,-50000) returns $60,604 … within rounding differences.
    =FV(3.922%,5,0,-50000) returns $60,604.

jimb

Wiki post about math functions

Threads with more details and math examples:

viewtopic.php?f=2&t=175496&p=2654945

viewtopic.php?f=2&t=197328&p=3014335#p3014335

viewtopic.php?f=11&t=196547&p=3003711#p3003711

viewtopic.php?f=2&t=150744&p=2258167#p2258167

poster #cruncher examples too.
viewtopic.php?f=2&t=194499#p2965797

post with lots of links to examples
viewtopic.php?f=2&t=184094&p=2797403#p2797403

About formula for Canadian mortgage
viewtopic.php?f=11&t=176445&p=2671543#p2671543

About Sallie Mae student loan, example of LOG function
viewtopic.php?f=2&t=183964&p=2790139#p2790139

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Abe
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Re: Interest Rate Calculation

Postby Abe » Wed Jan 11, 2017 4:04 pm

At the end of 60 months you will have $60,604 and your original investment was $50k, so your return (interest rate) on the $50k for 60 months is 3.85%. I think. :happy
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jimb_fromATL
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Re: Interest Rate Calculation

Postby jimb_fromATL » Wed Jan 11, 2017 4:07 pm

Kevin M wrote: If you want to be really precise what you will want to do is a Internal Rate of Return. You will want to model every cash flow in and out. You will need a spreadsheet to calculate this.

I thought about taking an IRR approach. However, you can think of the loan plus savings account as a single entity in the cash flow analysis, which allows you to reduce the analysis to a single cash flow in of $50K and a single cash flow out of the final value of the savings account.


For fixed payments and equal payments at exactly equal periods -- the way loan payments are calculated -- You don't need to build tables for use IRR. You can get the same results using the PMT(), RATE(), and FV() functions that I described in my previous post in this thread.

XIRR is only necessary when the payment and periods are not exactly the same. Since it uses specific dates, it will virtually always give slightly different results than you'll get from using the 1/12 yearly rate per month for 12 equal periods per year.

In fact XIRR implies more precision than you actually have in most loans and investments. It will probably never give you an exact result for investments or payments that are made on an irregular schedule, because in most accounts such as loans as well as investments like 401(k)s the date the payment is mailed or withheld from your paycheck may be several days earlier than it is actually posted. And it can be a few weeks off in the case of payments on mortgages and other loans that post only on a scheduled date --such as the 1st-- regardless of when the payment is received.

jimb

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jimb_fromATL
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Re: Interest Rate Calculation

Postby jimb_fromATL » Wed Jan 11, 2017 4:09 pm

Abe wrote:At the end of 60 months you will have $60,604 and your original investment was $50k, so your return (interest rate) on the $50k for 60 months is 3.85%. I think. :happy


Plenty close enough.

=RATE(60, 0, 50000, -60603.77 ) * 12 returns 3.853% compounded monthly
or =RATE(5, 0, 50000, -60603.77) returns 3.922% compounded yearly.

jimb

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Abe
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Re: Interest Rate Calculation

Postby Abe » Wed Jan 11, 2017 4:21 pm

jimb_fromATL wrote:
Abe wrote:At the end of 60 months you will have $60,604 and your original investment was $50k, so your return (interest rate) on the $50k for 60 months is 3.85%. I think. :happy


Plenty close enough.

=RATE(60, 0, 50000, -60603.77 ) * 12 returns 3.853% compounded monthly
or =RATE(5, 0, 50000, -60603.77) returns 3.922% compounded yearly.

jimb


I'm old fashioned. Never did figure out how to use a spreadsheet. I use a Texas Instrument BAll Plus financial calculator: N=60, PV=$50k, FV=$60,603.92 and compute for I/Y 3.85% (rounded to 2 places). Whatever, we still come up with the same answer. :beer
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jimb_fromATL
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Re: Interest Rate Calculation

Postby jimb_fromATL » Wed Jan 11, 2017 4:48 pm

Abe wrote:
I'm old fashioned. Never did figure out how to use a spreadsheet. I use a Texas Instrument BAll Plus financial calculator: N=60, PV=$50k, FV=$60,603.92 and compute for I/Y 3.85% (rounded to 2 places). Whatever, we still come up with the same answer. :beer

The firmware algorithms in the handheld calculator use exactly the same iterative methods as the RATE function I've described in previous posts. In fact, there's a good chance that the software library functions they used in their hard-coded firmware are called PMT(), RATE(), FV() and NPER(). They've evolved as pretty much standard math library names for the algorithms since I first started programming in the 70s -- in the days of coal-fired computers*, in assembly language.

I still marvel at how quick and easy it is using these new-fangled spreadsheets.

jimb


* A lot of younger folks do not realize that while it does not come directly from coal these days, modern-day computers still use captive smoke within their innards to do the calculations. In fact you can sometimes see proof of this when something goes wrong. When you see the smoke escaping from a computer, it virtually always ceases working.

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Kevin M
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Re: Interest Rate Calculation

Postby Kevin M » Wed Jan 11, 2017 5:44 pm

jimb_fromATL wrote:
Kevin M wrote: If you want to be really precise what you will want to do is a Internal Rate of Return. You will want to model every cash flow in and out. You will need a spreadsheet to calculate this.

I thought about taking an IRR approach. However, you can think of the loan plus savings account as a single entity in the cash flow analysis, which allows you to reduce the analysis to a single cash flow in of $50K and a single cash flow out of the final value of the savings account.


For fixed payments and equal payments at exactly equal periods -- the way loan payments are calculated -- You don't need to build tables for use IRR.<snip>

Jim, you messed up your quotes. I did not post the first quote you attributed to me. I posted the second quote in response to the first quote by another poster. I had already solved the problem exactly as you've described using PMT, RATE and FV, as I posted early in the thread. I simply mentioned the XIRR solution to demonstrate that you'll get the same result if you frame the problem correctly.

Kevin
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dm200
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Re: Interest Rate Calculation

Postby dm200 » Thu Jan 12, 2017 1:15 pm

I am loaning $50K for 60 months at a simple interest rate of 5.25%, the monthly payment to me will be $949.30 (loan is highly secured).


FYI - By the way, using an industry specific loan calculator I have access to, my calculations for such a loan, using a 30 day month (360 day year) and with the first payment due exactly one month after disbursement, comes out with this exact monthly payment amount.

Using a 365 day year (as many or most consumer loans are done today), a loan issued today with the first payment in one month would have a payment of 949.24. To show the affect of payments being made each month, but with the first payment in 45 days, the payment would be 951.15. I don't know how possible or likely it may be that payments are made early or late, but if these are made - you may want to consider (if not already done so) precise (to the day) calculations of payments received (breaking down principal and interest). It seems to me that the time to make such provisions (if it is relevant) is now and not wait until there becomes an "issue". If (depending on all the circumstances) you want to track payments to the day (and charge/credit interest) setting up a spreadsheet is not difficult. [I can give the details, if you should want]

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Re: Interest Rate Calculation

Postby MrDogg » Fri Jan 13, 2017 1:01 pm

To: dm200

The first loan payment will be received exactly one month from the day funds were disbursed and will arrive via automatic bank to bank transfer. Each subsequent payment will arrive on that same day each month. Since this transaction is between trusted friends neither one of us is concerned about any nickels and dimes affecting the payment based on esoteric calculation methods. But you do make an interesting point relative to this discussion.

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dm200
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Re: Interest Rate Calculation

Postby dm200 » Fri Jan 13, 2017 2:44 pm

MrDogg wrote:To: dm200
The first loan payment will be received exactly one month from the day funds were disbursed and will arrive via automatic bank to bank transfer. Each subsequent payment will arrive on that same day each month. Since this transaction is between trusted friends neither one of us is concerned about any nickels and dimes affecting the payment based on esoteric calculation methods. But you do make an interesting point relative to this discussion.


For the specific reasons you cite, I agree that these calculation issues/differences are irrelevant; it is only nickels and dimes. Where this might become relevant, perhaps, in your case is if the borrower wanted to pay off the loan in full early. For those who do this kind of "loan", it is not uncommon that they do not take these things into consideration and then, perhaps, have somewhat of a mess. Below is the amortization schedule for your loan. Using this 30 day month (30 day year) calculation, there are no interest/payment calculation differences for which month and day the loan is disbursed.

Code: Select all

Entry Date       Days      Payment    Principal    Interest  Life Ins   Dis Ins      Escrow      Balance
----- ---------- ---- ------------ ------------ ----------- --------- --------- ----------- ------------
 ORIG 01/13/2017                                                                              $50,000.00
    1 02/13/2017   30      $949.30      $730.55     $218.75     $0.00     $0.00       $0.00   $49,269.45
    2 03/13/2017   30      $949.30      $733.75     $215.55     $0.00     $0.00       $0.00   $48,535.70
    3 04/13/2017   30      $949.30      $736.96     $212.34     $0.00     $0.00       $0.00   $47,798.74
    4 05/13/2017   30      $949.30      $740.18     $209.12     $0.00     $0.00       $0.00   $47,058.56
    5 06/13/2017   30      $949.30      $743.42     $205.88     $0.00     $0.00       $0.00   $46,315.14
    6 07/13/2017   30      $949.30      $746.67     $202.63     $0.00     $0.00       $0.00   $45,568.47
    7 08/13/2017   30      $949.30      $749.94     $199.36     $0.00     $0.00       $0.00   $44,818.53
    8 09/13/2017   30      $949.30      $753.22     $196.08     $0.00     $0.00       $0.00   $44,065.31
    9 10/13/2017   30      $949.30      $756.51     $192.79     $0.00     $0.00       $0.00   $43,308.80
   10 11/13/2017   30      $949.30      $759.82     $189.48     $0.00     $0.00       $0.00   $42,548.98
   11 12/13/2017   30      $949.30      $763.15     $186.15     $0.00     $0.00       $0.00   $41,785.83
----- ---------- ---- ------------ ------------ ----------- --------- --------- ----------- ------------
 2017                   $10,442.30    $8,214.17   $2,228.13     $0.00     $0.00       $0.00             
----- ---------- ---- ------------ ------------ ----------- --------- --------- ----------- ------------
   12 01/13/2018   30      $949.30      $766.49     $182.81     $0.00     $0.00       $0.00   $41,019.34
   13 02/13/2018   30      $949.30      $769.84     $179.46     $0.00     $0.00       $0.00   $40,249.50
   14 03/13/2018   30      $949.30      $773.21     $176.09     $0.00     $0.00       $0.00   $39,476.29
   15 04/13/2018   30      $949.30      $776.59     $172.71     $0.00     $0.00       $0.00   $38,699.70
   16 05/13/2018   30      $949.30      $779.99     $169.31     $0.00     $0.00       $0.00   $37,919.71
   17 06/13/2018   30      $949.30      $783.40     $165.90     $0.00     $0.00       $0.00   $37,136.31
   18 07/13/2018   30      $949.30      $786.83     $162.47     $0.00     $0.00       $0.00   $36,349.48
   19 08/13/2018   30      $949.30      $790.27     $159.03     $0.00     $0.00       $0.00   $35,559.21
   20 09/13/2018   30      $949.30      $793.73     $155.57     $0.00     $0.00       $0.00   $34,765.48
   21 10/13/2018   30      $949.30      $797.20     $152.10     $0.00     $0.00       $0.00   $33,968.28
   22 11/13/2018   30      $949.30      $800.69     $148.61     $0.00     $0.00       $0.00   $33,167.59
   23 12/13/2018   30      $949.30      $804.19     $145.11     $0.00     $0.00       $0.00   $32,363.40
----- ---------- ---- ------------ ------------ ----------- --------- --------- ----------- ------------
 2018                   $11,391.60    $9,422.43   $1,969.17     $0.00     $0.00       $0.00             
----- ---------- ---- ------------ ------------ ----------- --------- --------- ----------- ------------
   24 01/13/2019   30      $949.30      $807.71     $141.59     $0.00     $0.00       $0.00   $31,555.69
   25 02/13/2019   30      $949.30      $811.24     $138.06     $0.00     $0.00       $0.00   $30,744.45
   26 03/13/2019   30      $949.30      $814.79     $134.51     $0.00     $0.00       $0.00   $29,929.66
   27 04/13/2019   30      $949.30      $818.36     $130.94     $0.00     $0.00       $0.00   $29,111.30
   28 05/13/2019   30      $949.30      $821.94     $127.36     $0.00     $0.00       $0.00   $28,289.36
   29 06/13/2019   30      $949.30      $825.53     $123.77     $0.00     $0.00       $0.00   $27,463.83
   30 07/13/2019   30      $949.30      $829.15     $120.15     $0.00     $0.00       $0.00   $26,634.68
   31 08/13/2019   30      $949.30      $832.77     $116.53     $0.00     $0.00       $0.00   $25,801.91
   32 09/13/2019   30      $949.30      $836.42     $112.88     $0.00     $0.00       $0.00   $24,965.49
   33 10/13/2019   30      $949.30      $840.08     $109.22     $0.00     $0.00       $0.00   $24,125.41
   34 11/13/2019   30      $949.30      $843.75     $105.55     $0.00     $0.00       $0.00   $23,281.66
   35 12/13/2019   30      $949.30      $847.44     $101.86     $0.00     $0.00       $0.00   $22,434.22
----- ---------- ---- ------------ ------------ ----------- --------- --------- ----------- ------------
 2019                   $11,391.60    $9,929.18   $1,462.42     $0.00     $0.00       $0.00             
----- ---------- ---- ------------ ------------ ----------- --------- --------- ----------- ------------
   36 01/13/2020   30      $949.30      $851.15      $98.15     $0.00     $0.00       $0.00   $21,583.07
   37 02/13/2020   30      $949.30      $854.87      $94.43     $0.00     $0.00       $0.00   $20,728.20
   38 03/13/2020   30      $949.30      $858.61      $90.69     $0.00     $0.00       $0.00   $19,869.59
   39 04/13/2020   30      $949.30      $862.37      $86.93     $0.00     $0.00       $0.00   $19,007.22
   40 05/13/2020   30      $949.30      $866.14      $83.16     $0.00     $0.00       $0.00   $18,141.08
   41 06/13/2020   30      $949.30      $869.93      $79.37     $0.00     $0.00       $0.00   $17,271.15
   42 07/13/2020   30      $949.30      $873.74      $75.56     $0.00     $0.00       $0.00   $16,397.41
   43 08/13/2020   30      $949.30      $877.56      $71.74     $0.00     $0.00       $0.00   $15,519.85
   44 09/13/2020   30      $949.30      $881.40      $67.90     $0.00     $0.00       $0.00   $14,638.45
   45 10/13/2020   30      $949.30      $885.26      $64.04     $0.00     $0.00       $0.00   $13,753.19
   46 11/13/2020   30      $949.30      $889.13      $60.17     $0.00     $0.00       $0.00   $12,864.06
   47 12/13/2020   30      $949.30      $893.02      $56.28     $0.00     $0.00       $0.00   $11,971.04
----- ---------- ---- ------------ ------------ ----------- --------- --------- ----------- ------------
 2020                   $11,391.60   $10,463.18     $928.42     $0.00     $0.00       $0.00             
----- ---------- ---- ------------ ------------ ----------- --------- --------- ----------- ------------
   48 01/13/2021   30      $949.30      $896.93      $52.37     $0.00     $0.00       $0.00   $11,074.11
   49 02/13/2021   30      $949.30      $900.85      $48.45     $0.00     $0.00       $0.00   $10,173.26
   50 03/13/2021   30      $949.30      $904.79      $44.51     $0.00     $0.00       $0.00    $9,268.47
   51 04/13/2021   30      $949.30      $908.75      $40.55     $0.00     $0.00       $0.00    $8,359.72
   52 05/13/2021   30      $949.30      $912.73      $36.57     $0.00     $0.00       $0.00    $7,446.99
   53 06/13/2021   30      $949.30      $916.72      $32.58     $0.00     $0.00       $0.00    $6,530.27
   54 07/13/2021   30      $949.30      $920.73      $28.57     $0.00     $0.00       $0.00    $5,609.54
   55 08/13/2021   30      $949.30      $924.76      $24.54     $0.00     $0.00       $0.00    $4,684.78
   56 09/13/2021   30      $949.30      $928.80      $20.50     $0.00     $0.00       $0.00    $3,755.98
   57 10/13/2021   30      $949.30      $932.87      $16.43     $0.00     $0.00       $0.00    $2,823.11
   58 11/13/2021   30      $949.30      $936.95      $12.35     $0.00     $0.00       $0.00    $1,886.16
   59 12/13/2021   30      $949.30      $941.05       $8.25     $0.00     $0.00       $0.00      $945.11
   60 01/13/2022   30      $949.24      $945.11       $4.13     $0.00     $0.00       $0.00        $0.00
----- ---------- ---- ------------ ------------ ----------- --------- --------- ----------- ------------
 2021                   $12,340.84   $11,971.04     $369.80     $0.00     $0.00       $0.00             
----- ---------- ---- ------------ ------------ ----------- --------- --------- ----------- ------------
Total                   $56,957.94   $50,000.00   $6,957.94     $0.00     $0.00       $0.00             
----- ---------- ---- ------------ ------------ ----------- --------- --------- ----------- ------------


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