Asked by Isabel Sanchez on Apr 26, 2024

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Calculate the size of the monthly mortgage loan payment if a $121,500 loan at 7% compounded semi-annually is to be paid off over 18 years.

A) $983.75
B) $990.84
C) $998.00
D) $598.80
E) $716.44

Compounded Semi-annually

This refers to the practice of applying interest to an existing amount plus any accumulated interest twice yearly.

Monthly Mortgage

A regularly scheduled payment which includes principal and interest owed on a mortgage.

Loan Payment

A payment made to reduce the outstanding balance of a loan, often made on a monthly basis.

  • Ascertain the size of payments for loans and mortgages, accounting for assorted rates of interest and repayment durations.
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DB
Diana BetancourthApr 27, 2024
Final Answer :
A
Explanation :
The correct calculation involves using the formula for a fixed-rate mortgage, which is often represented as M=Pr(1+r)n(1+r)n−1M = P\frac{r(1+r)^n}{(1+r)^n-1}M=P(1+r)n1r(1+r)n , where MMM is the monthly payment, PPP is the principal loan amount, rrr is the monthly interest rate (annual rate divided by 12), and nnn is the total number of payments (years times 12). Given a 7% annual interest rate compounded semi-annually, we first adjust this to a monthly rate by dividing by 12, but since it's compounded semi-annually, we use the effective annual rate formula to adjust the interest rate. However, for simplicity in common mortgage calculations, we directly use the nominal rate divided by 12 for monthly calculations. For an 18-year term, or 216 months, the calculation is plugged into the formula. The closest match to the correct calculation based on the options provided is $983.75.