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.Amir's monthly payment will be approximately

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To calculate Amir's monthly mortgage payment, we use the formula for a fixed-rate mortgage, which is often derived from the present value of an annuity formula. Given a principal amount (P) of $250,000, an annual interest rate (r) of 9% compounded semi-annually, and an amortization period of 25 years with monthly payments, we first adjust the annual interest rate for monthly compounding. The monthly interest rate (i) is 9%/2 (for semi-annual compounding) divided by 6 (to adjust to a monthly rate), which gives us 0.375%. The total number of payments (n) is 25 years * 12 months/year = 300 payments. The formula for the monthly payment (M) is:$$M = P\frac{i(1+i)^n}{(1+i)^n-1}$$Plugging in the values:$$M = 250,000\frac{0.00375(1+0.00375)^{300}}{(1+0.00375)^{300}-1}$$This calculation results in a monthly payment of approximately $2,069.94, which matches option A.

Amir Has Obtained a $250,000 Mortgage