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Lump-sum debt paydown versus saving and investing

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This week we're going to figure out how much I'll still owe on my mortgage in a decade if I use the inheritance I received from Aunt Matilda to pay it down faster.


Building off the last couple of articles, we're going to stick with my mortgage. To recap, here are the pertinent details:

I put $100,000 down and borrowed $350,000 to buy a house 34 months ago. The mortgage amortizes fully over 30 years, has monthly payments of $2,241.09,and the rate is 6.625%. I still owe $338,465.83, and thanks to a generous inheritance from my late Aunt Matilda, I have $100,000 to use to help me with my mortgage.

I'm going to imagine myself 10 years in the future, and figure out what my situation looks like if I handle things in different ways.

As you may recall from last week's article, if I continue to pay down my mortgage as required by the bank, after 10 more years, I'll owe $275,309.25.

a) If I use my inheritance to pay $100,000 down on my mortgage today, and then continue to make my normal monthly payments for the next 10 years, how much will I owe?

The next two problems assume that instead of using my $100,000 to pay down my mortgage, I invest them for growth and then use the resulting balance to pay down my mortgage after 10 years.

b) If I stick my inheritance in a 10-year Certificate of Deposit (CD) earning 2.00% interest, compounding monthly (which is about the highest I could find online today), how much would I be able to withdraw after 10 years?Assume that you get 2.00% interest after taxes and fees and that the rate is consistent (CD rates generally are).

c) If I use my inheritance to buy mutual funds that go up in value at a rate of 10% per year, how much will I be able to sell them for after 10 years? (Assuming that the 10% is after taxes and fees and that the return is consistent.)


a) N is 120 (12 months per year x 10 years), I/YR is 6.625%, PV is $238,465.83 (my current balance, less my $100,000 inheritance), PMT is $2,241.09. Solving for FV, I find that after 10 more years, I'll owe $22,353.32. Wow, that thing's nearly paid off! Doing the same kind of calculation I did before, I find that if I use the inheritance, I'll owe $252,955.93 less than if I didn't use it. That means that my $100,000 expenditure saved me $151,955.93 ($255,955.93 - $100,000).

b) The CD compounds monthly, so N is 120, I/YR is 2, PV is -$100,000, and PMT is $0 (they don't distribute the interest to me until the end of the 10 years). When I solve for FV, I find that my $100,000 account has the princely sum of $122,119.94 in it. It looks like paying down my mortgage would have had the inheritance earning nearly 7 times as much for me. Why do I say that?Paying down resulted in $151,955.93 in savings, and the CD only resulted in $22,119.94 in interest earnings.$151,955.93 divided by $22,119.94 is 6.87 - so paying down my higher-interest mortgage made me 6.87 times as much money as putting the money into a lower-yield CD.

c) Since the investment is growing at an annualized rate of 10%, I set P/YR to 1 (annual compounding). N is 10 (1 compounding period per year x 10 years), I/YR is 10, PV is -$100,000, and PMT is 0 (I'm not buying more mutual funds or selling anything I've got until the end of the 10 years). When I solve for FV, I find that I can sell my mutual funds for $259,374.25.

The interesting part of this result for me is the small size of the difference is between the amount I earn on the inheritance when earning 10%, compounded annually versus when I use it to accelerate my 6.625% monthly-compounding mortgage amortization. The difference ($259,374.25 - $252,955.93 = $6,418.32) is actually a lot smaller than I anticipated, because the 10% yield sounds a lot higher than my 6.625% mortgage interest rate.

Whew! That was a bit more involved! Next week, we'll discuss using investment income to assist with mortgage paydown! If you have any questions, please feel free to leave a comment and ask.

See you next time!