Question

Question 3: Floating Rate Mortgage

John is planning to buy a house worth $450,000, has $100,000 in savings that he will use as adown-payment and will borrow the remainder via a mortgage. He selects a floating rate, closed mortgage with a 3 year term and 25 year amortization period. He will make monthly payments and be charged an interest rate of 3.35% p.a., compounded semi-annually.

Part A: How much will John owe after 1 year has passed if interest rates do not change?

Part B: How much will John owe at the end of his term if, after 1 year, interest rates rise to 3.65%p.a., semi-annual compounding? What fraction of his payments went to principal and what fraction went to interest?

Answer 1

Monthly equivalent rate applicable to APR of 3.35% compounded semi annually= ((1+3.35%/2)^2)^(1/12)-1 = 0.277238%

Monthly equivalent rate applicable to APR of 3.65% compounded semi annually= ((1+3.65%/2)^2)^(1/12)-1 = 0.301879%

Part A: Money that John owe after 1 year has passed if interest rates do not change= $340,867.37

Part B:

Money that John owe at the end of his term if, after 1 year, interest rates rise to 3.65%p.a., semi-annual compounding= $322,368.32

Fraction of his payments went to principal = 43.72152%

Fraction of his payments went to interest= 56.27848%

Calculation as below: