Gavin and Holly purchased a $640,000 condominium in Toronto. They paid 20% of th
ID: 2521312 • Letter: G
Question
Gavin and Holly purchased a $640,000 condominium in Toronto. They paid 20% of the amount as a down payment and secured a 25-year mortage for the balance. They negotiated a fixed interest rate of 2.7% compounded semi-annually for a 5-year term with repayments made at the end of every month. Their mortgage contract also stated that they may prepay up to 15% of the original principal every year without at interest penalty. At the end of the first year, in addition to the regular monthly payment, they made a lump-sum payment of $22,000.
a. What was the size of the monthly payment?
Round to the nearest cent
b. What was the principal balance at the end of the first year?
Round to the nearest cent
c. By how much did the amortization period shorten after they made the lump sum payment at the end of the first year?
months
Explanation / Answer
The effective interest rate per month = 2.7%/ 6 month = 0.45 % per month
PVAF = ( 0.45%, 60) ( 5 year * 12 month each year = 60 payments)
= 52.48
Outstanding Amount at the beginning of first year
Total Cost- Down payment
= $ 640000- (20% of 640000)
= $ 512000
1) Monthly Payment = Net Outstanding Amount/ PVAF
= $ 512000/ 52.48
= $ 9756
Total payment in first year = ($ 9756 * 12 months) + $ 22000
= $ 117073 + 22000
= $ 139073
2) Outstanding Amount at the end of first year or beginning of second year
= $ 512000- 139073.
=. $ 372927
3). Revised Monthly payments
PVAF = (0.45%, 48) [12 month * 4 year = 48 payments ]
= 43.08
Monthly payments = $ 372927/ 43.08
= $ 8656.62 per month
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