Question

7. (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? (1 point)

(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 1? (Hint: Go to the TVM lecture notes for multiple cash flows and go to slide 15.) (1 point)

Answer 1

The monthly Payment can be found out using the annuity formula:

$PV=PMT \times \frac{1-(1+\frac{r}{frequency})^{-n\times frequency}}{\frac{r}{frequency}}$

Here PV is the loan amount, PMT is the monthly payment, r is the annual interest rate, frequency = 12 as we have monthly payment and n = 2 years or loan period

$1000=PMT \times \frac{1-(1+\frac{0.12}{12})^{-2\times12}}{\frac{0.12}{12}}$

When payments are made annually, the interest is also charged annually on the opening balance of the loan. As in year 1 the entire loan was due, the interest for the year would be rate x loan opening balance = 0.12 x 1000 = $120