Question

A homeowner borrows $300,000 over a 15-year mortgage term, fully amortising and payable monthly, at an interest rate of 4.5% per year fixed for 6 years, and is charged a closing fee of 2% on the principal sum.

a)       What is the monthly repayment amount for the initial 6-year period?

b)      What is the APR (annual percentage rate) over the full loan term?

At the expiry of the 6-year interest period, the interest rate changes to 5.5% for the remainder of the loan.

c)       What is the principal balance at the end of the 6-year period?

d)      What is the monthly repayment amount for the remainder of the loan?

e)      How much interest would be saved over the remainder of the loan if the homeowner chooses to repay an extra $100 a month on top of the above repayment amount?

Answer 1

a)What is the monthly repayment amount for the initial 

6-year period?

ANSWER

$1,814.45

 

WORKING

4.5% = 0.045

0.045/12 = 0.00375

P = 300000

N = 15*12i = 0.00375

 

c = P*i*((1+i)^N)/((1+i)^N-1)

c = $1,814.45   

 

b)What is the APR (annual percentage rate) over the full loan 

term?

ANSWER

4.735%

 

WORKING

4.5% = 0.045

0.045 + 2% = 0.065

0.065/12 = 0.00542

P = 300000

N = 15*12i = 0.00542

c = P*i*((1+i)^N)/((1+i)^N-1)

c = $2,011.01

APR = c*12 - P/NAPR = 4.735%

 

 

 

c)  What is the principal balance at the end of the 

6-year period?

ANSWER

$267,859.03

 

WORKING

4.5% = 0.045

0.045/12 = 0.00375

P = 300000

N = 15*12i = 0.00375

c = P*i*((1+i)^N)/((1+i)^N-1)

c = $1,814.45

P6 = P(1+i)^(N-6N) - c(1+i)^(N-6N-1)

P6 = $267,859.03

 

d) What is the monthly repayment amount for the remainder of the loan?

ANSWER

$2,067.91

 

WORKING

5.5% = 0.0550.055/12 = 0.00458

P = 300000

N = 15*12i = 0.00458

c = P*i*((1+i)^N)/((1+i)^N-1)

c = $2,067.91

 

 

e) How much interest would be saved over the remainder of 

the loan if the homeowner chooses to repay an extra $100 a month on top of the above repayment amount?

ANSWER

$40,767.61

 

WORKING

5.5% = 0.055

0.055/12 = 0.00458

P = 300000

N = 15*12i = 0.00458

c = P*i*((1+i)^N)/((1+i)^N-1)

c = $2,067.91

$100/month extra repayments

c = $2,167.91P9 = P(1+i)^(N-9N) - c(1+i)^(N-9N-1)

P9 = $259,232.39

Interest saved = $40,767.61