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## Lump-sum debt paydown versus saving and investing

Note: You can use any financial calculator to do this problem, but if you want the BEST, you can get our 10bii Financial Calculator for iOS, Android, Mac, and Windows!

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.

THE SCENARIO:

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.)

THE SOLUTION:

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!