Question

A foreign investor borrowed $36 million for the acquisition of a 180,000 square foot shopping center in Boulder, Colorado at a purchase price of $54 million. The mortgage loan was a 30-year fully amortizing fixed rate loan at a stated annual interest rate of 5% payable monthly and the borrower was charged 2 points by the lender at closing.

What was the effective annual interest rate on the loan if the loan was carried to maturity?

What was the effective annual interest rate on the loan if the principal balance was fully repaid at the end of 10 years?

Answer 1

All fianncials below are in $ mn.

Payment frequency is monthly. Hence, one period is one month. We will use the RATE function to calculate the effective rate per period. We will then convert the effective rate into effective annual rate.

PV = - Loan amount = - (36 - closing charges) = - 36 x (1 - 2%) = - 35.28

PMT = payment per period = 5% / 12 x $ 36 mn = 0.15

FV = Future redemption value = 36

What was the effective annual interest rate on the loan if the loan was carried to maturity?

Period = 30 years = 12 x 30 = 360 months

Hence, effective interest rate per month = Rate (Period, PMT, PV, FV) = RATE (360, 0.15, - 35.28, 36) = 0.4276%

Hence, effective annual interest rate = (1 + 0.4276%)¹² - 1 = 5.25%

What was the effective annual interest rate on the loan if the principal balance was fully repaid at the end of 10 years?

Now, Period = 10 years = 12 x 10 = 120 months

Hence, effective interest rate per month = Rate (Period, PMT, PV, FV) = RATE (120, 0.15, - 35.28, 36) = 0.4381%

Hence, effective annual interest rate = (1 + 0.4381%)¹² - 1 = 5.39%