A couple needs a mortgage of $300,000. Their mortgage broker presents them with two options: a 30-year mortgage at 8 1/2%

interest or a 15-year mortgage at 7 3/4%
interest. (Round your answers to the nearest cent.)
(a) Find the monthly payment on the 30-year mortgage and on the 15-year mortgage.
30-year $
15-year $

b) Find the total amount to be paid over the life of the 30-year mortgage and on the 15-year mortgage.
30-year $
15-year $

5 consecutive problems from a variety of topics

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To find the monthly payment on each mortgage, we can use the formula for calculating the mortgage payment:

M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:
M = monthly payment
P = principal (loan amount)
r = monthly interest rate
n = number of payments (in months)

For the 30-year mortgage:
Principal (P) = $300,000
Interest rate (r) = 8 1/2% = 8.5% = 0.085
Number of payments (n) = 30 years * 12 months/year = 360 months

Now, let's calculate the monthly payment for the 30-year mortgage:

M = $300,000 * (0.085 * (1 + 0.085)^360) / ((1 + 0.085)^360 - 1)

Using a calculator or a spreadsheet, the monthly payment for the 30-year mortgage is approximately $2,313.22.

For the 15-year mortgage:
Principal (P) = $300,000
Interest rate (r) = 7 3/4% = 7.75% = 0.0775
Number of payments (n) = 15 years * 12 months/year = 180 months

Now, let's calculate the monthly payment for the 15-year mortgage:

M = $300,000 * (0.0775 * (1 + 0.0775)^180) / ((1 + 0.0775)^180 - 1)

Using a calculator or a spreadsheet, the monthly payment for the 15-year mortgage is approximately $2,745.77.

(a) The monthly payment on the 30-year mortgage is $2,313.22 and the monthly payment on the 15-year mortgage is $2,745.77.

To find the total amount to be paid over the life of each mortgage, we can multiply the monthly payment by the number of payments.

For the 30-year mortgage:
Total amount = $2,313.22 * 360 months

Using a calculator or a spreadsheet, the total amount to be paid over the life of the 30-year mortgage is approximately $832,363.20.

For the 15-year mortgage:
Total amount = $2,745.77 * 180 months

Using a calculator or a spreadsheet, the total amount to be paid over the life of the 15-year mortgage is approximately $494,038.60.

(b) The total amount to be paid over the life of the 30-year mortgage is $832,363.20 and the total amount to be paid over the life of the 15-year mortgage is $494,038.60.