Final answer:
To determine the monthly payment for a mortgage loan, the loan amount, interest rate, and loan term are used in a formula that incorporates the semi-annual compounding to find the equivalent monthly rate. Using these, the monthly payment can be calculated.
Step-by-step explanation:
To calculate the monthly mortgage payment on a $121,500 loan at 7% interest compounded semi-annually over 18 years, we need to convert the semi-annual rate to a monthly rate and apply the formula for an amortizing loan payment. The formula used is:
PMT = P * r * (1 + r)^n / [(1 + r)^n - 1]
Where PMT is the monthly payment, P is the principal amount ($121,500), r is the monthly interest rate, and n is the total number of payments.
First, we convert the annual interest rate to a semi-annual rate, and then to a monthly rate since the compounding is semi-annual:
Annual rate (nominal) = 7%
Semi-annual rate = 7% / 2 = 3.5%
Monthly rate = (1 + 0.035)^(1/6) - 1
Next, we calculate the number of monthly payments:
n = 18 years * 12 months/year = 216 months
Using these values, we substitute into the loan payment formula to find the monthly payment.