Question

Suppose you have $250,000 of loan. The terms of the loan are that the yearly interest is 6% compounded quarterly. You are to make equal quarterly payments of such magnitude as to repay this loan over 30 years.

(Keep all your answers to 2 decimal places, e.g. XX.12.)

(a) How much are the quarterly payments? Ans: 4504.63

(b)  After 5 years' payments, what principal remains to be paid? Ans: 232550.19

(c) How much interest is paid in the first quarter of the 6^th year? Ans: 3488.25

(d) How much is the total interest paid over the 30 years? Ans: 290555.60

(e) If you have a lump sum payment of $20,000 at the end of 5 years, and maintain the same level of quarterly payment, when will you pay off your loan, i.e. how many years in total will you pay off the loan?

Need help with part (e). Thanks!

Answer 1

Step 1. For the solution to question 5, let us look at the principal outstanding at the end of 19th quarter. I have used MS excel to solve this. . Use the FV function to calculate the principal at the end of 19th quarter as below

=FV(6%/4,19,-4504.63,250000)

This gives us the value of $ 233551.54 at the end of 19th quarter

Step 2. Now at the end of 5 yr i.e in 20th quarter there is lump sum repayment of $20,000 in addition to the normal repayment from installment. The installment would consist of interest payment and then repayment

Interest payment in 20th quarter is 6%*233551.54/4 = $ 3503.27 . After subtracting this from installment we get normal repayment of 1001.36.

Hence total repayment in 20th quarter is $ 20,000 + $ 1001.36 = $21,001.36

Outstanding balance at the end of 20th quarter = $212550.19.

Step 3 - Now the outstanding principal of $ 212550.19 has to repaid using normal installments . Using the NPER function in excel as follows

=NPER(6%/4,4504.63,-(233551-20000-1001.36),,) we get the remaining number of quarters as 82.62

Adding this to the initial 20 quarters we get 102.62 quarters as the total number of quarters to repay the loan

converting this into years, ~ 25.65 years are needed to repay the loan