A mortgage of $300,000 is taken at 4.50% compounded semi-annually with monthly payments. If the amortization period is 20 years, what is the monthly mortgage payment?

Question: A mortgage of $300,000 is taken at 4.50% compounded semi-annually with monthly payments. If the amortization period is 20 years, what is the monthly mortgage payment?

Answer options:

• $1,897.43 ✅ $1,933.27
• $2,012.50
• $2,050.00

Correct answer: $1,933.27

Explanation: First, calculate the effective monthly interest rate: (1 + 0.045/2)^2 = (1 + i_monthly)^12. So, i_monthly = (1 + 0.045/2)^(2/12) - 1 = (1.0225)^(1/6) - 1 ≈ 0.0037156. Then, use the mortgage payment formula: PMT = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ], where P = $300,000, i = 0.0037156, and n = 20 * 12 = 240. PMT = $300,000 [ 0.0037156(1 + 0.0037156)^240 ] / [ (1 + 0.0037156)^240 – 1 ] = $1,933.27.