Simon has taken a 20-year, $252,000 mortgage on his house at an interest rate of 6% p.a., compounded annually. What is the outstanding balance of the mortgage after the payment of the fifth annual instalment?Group of answer choices$129,987.19$213,383.05$142,156.38$250,707.02
Question
Simon has taken a 20-year, 129,987.19142,156.38$250,707.02
Solution
To solve this problem, we need to use the formula for the outstanding balance of a mortgage, which is:
P = [r*PV / (1 - (1 + r)^-n)]
Where: P = payment per period r = interest rate per period PV = present value or initial loan amount n = number of periods
Given: PV = $252,000 r = 6% per annum = 0.06 n = 20 years
First, we need to calculate the annual payment (P).
P = [0.06 * 22,578.71
This is the annual payment Simon has to make.
The outstanding balance after the payment of the fifth annual instalment can be calculated using the formula for the outstanding balance of a loan, which is:
B = P / r * (1 - (1 + r)^-(n - t))
Where: B = outstanding balance t = number of periods elapsed
Given: t = 5 years
B = 213,383.05
So, the outstanding balance of the mortgage after the payment of the fifth annual instalment is $213,383.05.
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