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:
Note: Some of these numbers are slightly different than at the end of the previous posts. The reason for the discrepancies is that in this post, I've re-entered the PMT number to make sure that the calculator isn't using fractions of a penny in its calculations. Since we really pay $2,241.09 and not $2,241.08836 each month, some of the numbers later on in the calculation are going to be slightly different than what we calculated before.
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 $338,485.64, 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 $275,347.60.
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 $238,485.64 (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 $81,737.16. Wow, that paid off a lot more than $100,000! Doing the same kind of calculation I did before ($275,347.60 - $81,737.16 = $193,610.44) , I find that if I use the inheritance, I'll owe $193,610.44 less than if I didn't use it. That means that my $100,000 expenditure saved me $93,610.44 ($193,610.44 - $100,000.00).
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 over 4 times as much for me. Why do I say that? Paying down resulted in $93,610.44 in savings, and the CD only resulted in $22,119.94 in interest earnings. $93,610.44 divided by $22,119.94 is 4.23 - so paying down my higher-interest mortgage made me 4.23 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, of which $159,374.25 is profit. This is substantially higher than the amount paying down the mortgage saved me ($159,374.25 - $93,610.44= $65,763.81). Given that the 10% rate of return is substantially higher than the 6.625% rate of the mortgage, this isn't surprising.
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!
