Question

A building is purchased at $310,000 on terms of $60,000 down payment and 10 end-of-year mortgage payments of $37,257.27 per year in the next 10 years. Calculate the interest rate of this mortgage. 8. (a) If the annual interest rate is 6% and interest is compounded semiannually, what is the effective annual interest rate?

(b) If the annual interest rate is 9% and interest is compounded every four months (3 times a year), what is the effective annual interest rate?

(c) If the annual interest rate is 7.25% and interest is compounded every three months (4 times a year), what is the effective annual interest rate?

Answer 1

Effective Annual Interest Rate (EAR) = (1+(r/m))^n*m -1

r = annual interest rate

n = number of years

m = number of periods in a year

a. EAR = (1+(0.06/2))² -1 = 6.09%

b. EAR = (1+(0.09/3))³ -1 = 9.27%

c. EAR = (1+(0.0725/4))⁴ -1 = 7.45%

Purchase Price = $310000

Down Payment = $60000

Loan Amount = $310000-$60000 = $250000

Time period = 10 years

Mortgage Payment per year = $37257.27

Using Annuity Formula

250000 = (37257.27/r)[1-(1/(1+r)¹⁰)]

By using Hit and Trial

using r = 8%

= (37257.27/0.08)[1-(1/(1.08)¹⁰)]

= 250000

So Interest Rate on Mortgage = 8%