Question

9. (a) Assume that you have borrowed $1,000 for 2 years and you have an annual interest rate of 12% (annually compounded). What is the monthly payment due on the loan? (b) Switch gears here and now assume that the payments are made annually. What is the annual interest expense for the borrower, and the annual interest income for the lender, during Year 12 (Hint: Go to the TVM lecture notes for multiple cash flows and go to slide 15.)

Answer 1

Q 9 a)

Amount borrowed = PV = $ 1000
number of years = 2
Interest rate = 12 % ( compounded annually)
Interest rate / month 12 % / 12 = 1 %

Number of payments = N = 2 x 12 = 24
Payment / month = $ 47.07

Q 9 b)

payments are made annually
Amount borrowed = $ 1000
Number of payments = 2
interest rate = 12 %

Payments to be made = 591.7 / year
Interest expense after year 1 = $ 1000 x ( 1.12) - $ 1000 = $ 1120 - $ 1000 = $ 120

Annual interest expense for year 1 for the borrower = $ 120
Principal amount for 1st year = $ 471.70
Annual interest expense for year 2 for the borrower = $ 63.40
Principal amount for 2nd year = $ 528.30

Total interest expense = $ 120 + $ 63.40 = $ 183.30

We can see that the total amount of interest and principal payment = $ 120 + $ 471.70 = $ 63.40 + $ 528.30 = $ 591.7