Problem 49 Solution

One way of looking at the flaw in his logic is that he is assuming that you don't withdraw money from your investment to make the car payments. If you did you would have only $110.47 in the account after the 57th payment, with three full payments to go.

However, if you were willing to not touch your investment and make the payments out of your pocket there is still a problem. You have to consider the time value of money. Lets assume inflation equal to the 6% interest rate, compounded monthly. The time value of the car payments made would be $10,364.77, however the time value of your $13,488.50 after five years would only be $10,000. In other words after five years your initial investment of $10,000 has gone down in value more than the interest savings.

Note: The payments on a loan of $x, at intrest rate i, over n periods is $xi/(1-vⁿ), where v=1/(1+i). In this case x=$10,000, i=.075/12=.00625, and n=60.

Michael Shackleford, A.S.A.