Amir has obtained a $250,000 mortgage.The mortgage is amortized over 25 years and the term of the mortgage is five years.The mortgage interest rate is 9% compounded semi-annually.Amir will begin making monthly payments at the end of the month.The monthly payment is closest to

Question

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To find the monthly payment, we can use the formula for mortgage payments:

P = (PV * r) / (1 - (1 + r)^(-n))

where P is the monthly payment, PV is the principal value of the mortgage, r is the monthly interest rate, and n is the total number of monthly payments over the term of the mortgage.

First, we need to find the mortgage balance after five years, which is the end of the term. To do this, we use the formula for compound interest:

FV = PV * (1 + r/2)^(2*t)

where FV is the future value of the mortgage after five years, t is the number of periods (which is 2*5 = 10 for semi-annual compounding), and r is the semi-annual interest rate (which is 0.09/2 = 0.045).

FV = 250000 * (1 + 0.045)^(2*5) = 362,187.22

So after five years, Amir's mortgage balance will be $362,187.22.

Next, we can use the mortgage payment formula with PV = $362,187.22, r = 0.09/12 = 0.0075 (the monthly interest rate), and n = 25*12 = 300 (the total number of monthly payments over 25 years).

P = (362187.22 * 0.0075) / (1 - (1 + 0.0075)^(-300)) = $2,069.94

Therefore, the monthly payment is closest to $2,069.94, which is choice (A).

Amir Has Obtained a $250,000 Mortgage