Question

18. You have graduated from college but unfortunately have $32,000 in outstand-ing loans. The loans require monthly payments of $3,245, which covers inter-est and principal repayment (that is, the loan has the same basic features as a mortgage). If the interest rate is 4 percent, how long will it take you to repay the debt? If the powers that be raise the rate to 6 percent, how many additional years will be required to retire the loans? Please break down answer into steps

Answer 1

Outstanding loan = 32000. Monthly payment = 3245. Rate of interest is 4% annually and 4%/12 = 0.33% per month. Number of months required for the loan to be paid off is found as

32000 = 3245 x (P/A, 0.333%, n)

32000/3245 = ((1.00333)^n - 1)/(0.00333*1.00333^n)

9.8613 = 300 - 300/1.00333^n

300/1.00333^n = 290.1387

This gives n = ln(300/290.1387)/ln(1.00333) = 10.044 months.

If the rate is now 6%/12 = 0.5 we have

32000 = 3245 x (P/A, 0.5%, n)

32000/3245 = ((1.005)^n - 1)/(0.005*1.005^n)

9.8613 = 200 - 200/1.005^n

200/1.005^n = 190.1387

This gives n = ln(200/190.1387)/ln(1.005) = 10.138 months.

There would be an additional 0.094 month or 3 days more.