Question

Anusha and Naveen are planning to buy their first home. They have saved $30,000 and will withdraw the maximum from their RRSPs under the Home Buyers’ Plan. They will pay the cost of CMHC mortgage loan insurance separately. They estimate closing costs at $8,200 and will take a 25-year mortgage at a rate of 3.2%, compounded semi-annually, for a 3-year term. They will pay the mortgage monthly. The home they wish to buy costs $450,000.

Part a

How much of a mortgage loan will the couple need?

Part b

How much will CMHC loan insurance cost?

Part c

What will be the couple’s monthly mortgage payment and loan balance at the end of their term?

Answer 1

The total house cost = (450000+8200) = $ 458200

Savings = $ 30000

Max RRSP withdrawal under Home Buyer's Plan = $50000 ($25000 each for Anusha and Naveen)

Hence there total non-mortgage funds are $80000 and they will have to borrow (458200-80000) = $378200. Note that we are given that they will pay the loan insurance cost separately hence not considered for our calculations.

CMHC loan insurance is the function of Loan To Value (LTV) - the LTV in this case will be = Loan Amount / House Cost which is 378200/450000 = 84.04% which will attract 2.80% premium which will be (2.80% * 378200) = $10589.6

Monthly Mortgage Payment formula:

MP = Loan Amount * [r * (1+r)^t?] / [(1+r)^t? - 1] where MP is the monthly payment, r is the monthly interest rate and t is the time period in months. We are given r as 3.2% compounded semi annually which means effective annual rate = (1+3.2%/2)²? - 1 = 3.2256% and monthly rate will be (3.2256%/12) = 0.2688%. The time period t in months is (25*12) = 300.

Hence MP = 378200 * [0.2688% * (1+0.2688%)³⁰⁰?] / [(1+0.2688%)³⁰⁰? - 1] = $ 1838.16

The formula for the loan balance at the end of month k is as below:

Remaining Loan = Loan * [ (1+r)^t - (1+r)^?k? ] / [(1+r)^t? - 1]? plugging in the values (k= 36 months)

Remaining Loan_?(k=36)? = 378200 * [(1+0.2688%)³⁰⁰ - (1+0.2688%)³⁶?] / [(1+0.2688%)³⁰⁰? - 1]? = $ 347189.3