213.6

6.Let's say you have a student loan at an interest rate of 6%, compounded monthly. As long as you're in school, you don't have to repay it. However, starting one month from graduation, you have to start repaying it.

1. Assume that your monthly payment will be 111.02 and you will have to make ten years of payments. What is the present value of your loan payments today, 1.5 years before graduation? (7 pts.)

The value of your loan on your graduation day will be:

\( \Large 111.02 \left [ \frac{1}{\frac{.06}{12}} - \frac{1}{\frac{.06}{12} \left(1+\frac{.06}{12} \right )^{120} } \right ] = 9{,}999.95 \).

The value today is:

\( \Large \frac{9999.95}{\left( 1 + \frac{.06}{12} \right)^{18}} = 9141.32\)

2. Imagine you have the opportunity to repay the loan in annual (instead of monthly) installments over the same length of time. If the first payment is due 1 year after graduation, would the payment amount be more or less than $1332.24? What if the first payment were due on graduation day? WHY? Explain with words, not math. (6 pts.)

$1332.24 is 12 times the monthly payment. We learned in class that if you wait one full year before making any payments, that annual payment will have to be more than just 12 times the monthly payments you would have made. The reason is that the bank is waiting to get its money and interest keeps accumulating on your principal. If you make monthly payments, you attack the principal immediately, reducing your total interest immediately.

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