Question

A family needs to take out a 15​-year home mortgage loan of

$100,000 through a local bank. Annual interest rates for 15​-year
mortgages at the bank are 7.5% compounded monthly.
​(Round the final

Answer 1

$871.90

Step-by-step explanation:

To calculate the monthly mortgage payment for a 15-year home mortgage loan of $100,000 with an annual interest rate of 7.5% compounded monthly, we can use the formula for the monthly mortgage payment:

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

Where:

M = Monthly mortgage payment

P = Principal amount (loan amount) = $100,000

r = Monthly interest rate = Annual interest rate / 12 / 100 = 7.5% / 12 / 100

n = Total number of monthly payments = 15 years * 12 months/year

Let's calculate the monthly mortgage payment:

r = 7.5% / 12 / 100 = 0.00625 (decimal form)

n = 15 years * 12 months/year = 180 months

M = $100,000 * (0.00625 * (1 + 0.00625)^180) / ((1 + 0.00625)^180 - 1)

Using a calculator or spreadsheet, the monthly mortgage payment comes out to be:

M ≈ $871.90 (rounded to the nearest cent)

Therefore, the monthly mortgage payment for a 15-year home mortgage loan of $100,000 at an annual interest rate of 7.5% compounded monthly is approximately $871.90.