Final answer:
To calculate monthly payments on a 30-year or 15-year mortgage of $80,000 at 9% interest, the formula for an amortizing loan is used, incorporating the principal, monthly interest rate, and number of payments. Calculating requires a financial calculator or a spreadsheet which applies the formula to determine precise payments.
Step-by-step explanation:
The question asks for the calculation of the monthly payment on a 30-year mortgage and a 15-year mortgage both for the principal amount of \$80,000 at an interest rate of 9%. To compute monthly mortgage payments, one can use the formula for an amortizing loan which is:
\( M = P \frac{r(1+r)^n}{(1+r)^n - 1} \)
Where:
- \(M\) is the total monthly payment.
- \(P\) is the principal amount (\$80,000).
- \(r\) is the monthly interest rate (annual rate divided by 12 months).
- \(n\) is the number of payments (terms in months).
First, we'll calculate for the 30-year mortgage. The monthly interest rate is 9% per annum, or 0.09/12 per month.
\(r = 0.09 / 12 = 0.0075\)
\(n = 30 \times 12 = 360\) payments
Using the formula, we get:
\( M = \$80,000 \frac{0.0075(1+0.0075)^{360}}{(1+0.0075)^{360} - 1} \)
For the 15-year mortgage, \( n = 15 \times 12 = 180 \) payments.
Use the same formula with the new \( n \) value to find the monthly payment.
Note: Complete calculation requires a financial calculator or spreadsheet program to determine the exact payment. This methodology will give you the monthly payment structure for both the 30-year term and the 15-year term.