Question

Ann obtains a $150,000, 20-year mortgage with a bank at 9% p.a., compounded monthly. a. What is her monthly repayment? b. Suppose that after 5 years, Ann plans to repay the loan by making an additional payment each month along with her regular payment. How much must Ann pay each month if she wishes to pay off the loan in 10 years?

Answer 1

Question a:

PV = Loan Amount = $150,000

n = 20*12 = 240 months

r = monthly interest rate = 9%/12 = 0.75%

Monthly payment = [r*PV] / [1 - (1+r)^-n]

= [0.75% * $150,000] / [1 - (1+0.75%)^-240]

= $1,125 / 0.833587155

= $1,349.58893

Therefore, monthly payment is $1,349.59

Question b:

P = Monthly payment = $1,349.59

n = 20*12 = 240 months

r = monthly interest rate = 9%/12 = 0.75%

x = loan payments made = 5*12 = 60 months

Remaining loan balance = P * [1 - (1+r)^-(n-x)] / r

= $1,349.59 * [1 - (1+0.75%)^-(240-60)] / 0.75%

= $1,349.59 * 0.739450566 / 0.0075

= $133,060.679

PV = Remaining balance after 5 years = $133,060.68

n1 = 10 *12 = 120 months

New monthly payment = [r * PV] / [1 - (1+r)^-n1]

= [0.75% * $133,060.68] / [1 - (1+0.75%)^-120]

= $997.9551 / 0.592062695

= $1,685.55646

= $1,685.56

Additional monthly payment = $1,685.56 - $1,349.59 = $335.97

Therefore, additional monthly payment if loan is repaid in 10 years is $335.97