Question

1. Hannah is planning to purchase her first home. She has spoken to the bank who has advised that she qualifies for a 25 year mortgage of $1,400,000 at an annual percentage rate of 6%. Payments will be made monthly and therefore interest will be compounded monthly. a. What is the effective annual rate on this loan?
   2. Calculate her monthly payment.
   3. Prepare an amortization schedule for the first two months of the loan.   

Answer 1

Effective annual rate = (1 + Annual rate / n)ⁿ , where n is the number of compunding periods.

Since the loan is compounded monthly, n = 12

Annual rate = 6%

Effective annual rate = (1 + 0.06/12)¹² - 1 = 0.06168 or 6.618%

a.

PV = P x [1 - (1 + r)^-n] / r

Where PV is the present value of the loan amount = 1,400,000

r is the monthly interest rate = 6/12 = 0.5%

n is the number of months = 25 x 12 = 300

P is the monthly payments

P = PV x r / [1 - (1 + r)^-n] = 1,400,000 x 0.005 / [1 - (1.005)^-300]

P = $9,020.22

b.

	1	2
Principal Remaining	$1,400,000	$1,397,979.78
Monthly Payment	$9,020.22	$9,020.22
Interest Payment	$7,000.000	$6,989.899
Principal Repayment	$2,020.22	$2,030.32

Interest payment in month 1 is 1,400,000 x 0.005 = 7,000

Principal repayment in month 1 is Monthly payment - interest payment = 2,020.22

Principal remaining in month 2 = Principal remaining in month 1 - principal repayment in month 1 = 1,397,979.78

Interest payment = 1,397,979.78 x 0.005 = 6989.899

Principal repayment = 9,020.22 - 6989.899 = 2,030.32