Final answer:
To find the monthly payment on a 30-year mortgage of $100,000 at 8% interest compounded monthly, divide the annual interest rate by 12, calculate the number of monthly payments, add 1 to the monthly interest rate, raise it to the power of the negative number of payments, and calculate the monthly payment by dividing the loan amount by the result. The monthly payment for this mortgage is approximately $432.90. The total amount paid on this loan over the 30-year period is $155,844.
Step-by-step explanation:
To calculate the monthly payment on a 30-year mortgage of $100,000 at 8% interest per year, compounded monthly, you can use the formula for monthly payments on an amortizing loan:
- First, convert the annual interest rate to a monthly interest rate. Divide the annual interest rate by 12 and convert it to a decimal: 8% / 12 = 0.08 / 12 = 0.0067.
- Next, calculate the number of monthly payments. Multiply the number of years (30) by 12: 30 * 12 = 360.
- Then, calculate the monthly interest rate plus one. Add 1 to the monthly interest rate: 0.0067 + 1 = 1.0067.
- After that, raise the result from step 3 to the power of the negative number of payments: (1.0067)^(-360) = 0.231.
- Finally, calculate the monthly payment using the loan amount and the result from step 4: $100,000 / 0.231 = $432.90 (rounded to the nearest cent).
The total amount paid on this loan over the 30-year period can be calculated by multiplying the monthly payment by the total number of payments: $432.90 * 360 = $155,844.