### Can someone check my math and my logic on this?

Posted:

**Mon Nov 16, 2020 5:37 pm**Hi. First post here, hope it isn't a bonehead one!

Without getting into too much detail at the moment, I want to make a comparison and I'm using hypothetical numbers. Let's say I have $100K in cash, and I also have a new debt of $100K that is to be paid over 10 years at 5% interest, which is a monthly payment of $1060. I'm trying to decide whether to pay the entire $100K up front and do away with the debt, or to take on the debt and invest the $100K. This is the way I was looking at it:

Option 1: Pay off the loan now and take the monthly payment I would have had ($1060) and invest it.

Option 2: Take on the debt and invest the $100K now, incurring the $1060 monthly payment.

How to compare? I made the assumption that an investment over 10 years would work out to 5% compounded interest through the stock market and other diversification. I chose 5% because it is the same as the interest on the debt and I just wanted to kind of compare apples to apples. The market typically would outperform 5% interest over 10 years or so (I know, no guarantee of that). I ran compound interest calculations that showed the $100K lump sum would be worth about $164K in 10 years. Interestingly, if I paid off the debt and assume that I make $1060 monthly investments starting from 0, I also end up at about $164K in 10 years ($1060/mo is about $127K in 10 years).

So I figure either way I'm going to end up with $164K in investment income (theoretically). With Option 1 I lose $100K for a net of $64K. With Option 2 I lose the principal AND interest to the creditor, which is $127K. So in that case my net is 164 - 127 = $37K. That would suggest that I should pay off the debt right away and hope I can beat the interest rate in the market or elsewhere.

I know there are other issues to consider, but mathematically am I looking at this in a reasonable way?

Without getting into too much detail at the moment, I want to make a comparison and I'm using hypothetical numbers. Let's say I have $100K in cash, and I also have a new debt of $100K that is to be paid over 10 years at 5% interest, which is a monthly payment of $1060. I'm trying to decide whether to pay the entire $100K up front and do away with the debt, or to take on the debt and invest the $100K. This is the way I was looking at it:

Option 1: Pay off the loan now and take the monthly payment I would have had ($1060) and invest it.

Option 2: Take on the debt and invest the $100K now, incurring the $1060 monthly payment.

How to compare? I made the assumption that an investment over 10 years would work out to 5% compounded interest through the stock market and other diversification. I chose 5% because it is the same as the interest on the debt and I just wanted to kind of compare apples to apples. The market typically would outperform 5% interest over 10 years or so (I know, no guarantee of that). I ran compound interest calculations that showed the $100K lump sum would be worth about $164K in 10 years. Interestingly, if I paid off the debt and assume that I make $1060 monthly investments starting from 0, I also end up at about $164K in 10 years ($1060/mo is about $127K in 10 years).

So I figure either way I'm going to end up with $164K in investment income (theoretically). With Option 1 I lose $100K for a net of $64K. With Option 2 I lose the principal AND interest to the creditor, which is $127K. So in that case my net is 164 - 127 = $37K. That would suggest that I should pay off the debt right away and hope I can beat the interest rate in the market or elsewhere.

I know there are other issues to consider, but mathematically am I looking at this in a reasonable way?