Question

A homeowner borrows $325,000 over a 25-year mortgage term, fully amortising and payable
monthly, at an interest rate of 3% per year fixed for 6 years, and is charged a closing fee of 3.5% 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 S100 a month on top of the above repayment amount?

Answer 1

a) Monthly payment for initial 6 years is $1,595

3.5% (3.5% * 3,25,000) = $11,375 closing fee is added in the total borrowings  

Principal + Closing fee = 3,25,000+11,375 =3,36,375

Rate is divided by 12 and period is multiplied by 12 for monthly compounding.

B) Annual Percentage Rate - Annual percentage rate refers to the annual rate of interest charged to borrowers and paid to investors. APR is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan or income earned on an investment. This includes any fees or additional costs associated with the transaction but does not take compounding into account. The APR provides consumers with a bottom-line number they can easily compare to rates from other lenders.

C) Principal balance at the end of 6th year is sum of all payment until 6th year - initial mortgage value

Sum of principal until 72nd Month (6th year) is 59,415

$3,36,375 - 59,415 = $2,76,960

D) Monthly payment stating 7th year would be $1,961

e) Interest saved would be Total interest paid without incremental $100 monthly payment - interest paid with $100 incremental monthly payment.

Sum of all interest payment = $1,70,048 - 1,54,376 = 15,672