Question

You have graduated from college but unfortunately have $27,000 in outstanding loans. The loans require monthly payments of $3,690, which covers interest 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? Use Appendix D to answer the question. Round your answer up to the next whole number. If the powers that be raise the rate to 7 percent, how many additional years will be required to retire the loans? Use Appendix D to answer the question. Round your answer up to the next whole number.

Answer 1

Loan Outstanding = $ 27000, Required Monthly Payments = $ 3690 and Interest Rate = 4 % per annum or (4/12) = 0.25 % per month

Let the number of months required be T

Therefore, 27000 = 3690 x (1/0.0025) x [1-{1/(1.0025)^(T)}]

[1-{1/(1.0025)^(T)}] = 0.018293

0.981707 = 1 / (1.0025)^(T)

(1.0025)^(T) = 1 / 0.981707 = 1.018634

= T

T = 7.39 months ~ 8 months

If the interest rate is raised to 7 % per annum then let the required time be T1

Monthly Rate = (7/12) = 0.5833 %

Therefore, 27000 = 3690 x (1/0.005833) x [1-{1/(1.005833)^(T1)}]

0.04268 =  [1-{1/(1.005833)^(T1)}]

1/(1.005833)^(T1) = 1-0.04268 = 0.95732

(1.005833)^(T1) = 1/0.95732 = 1.044583

T1 = = 7.4999 ~ 8 months

Number of additional years (or months) required to repay the loan if intrest rate is raised from 4 to 7 months is actually zero.