Answer:
To calculate the cost of the mortgage, we need to find the total amount that Sonya will pay back over the 25-year period.
One way to do this is to use the formula for the future value of an annuity, which is:
FV = Pmt x ((1 + r)^n - 1) / r
where FV is the future value, Pmt is the periodic payment, r is the interest rate per period, and n is the number of periods. In this case, we want to find the total future value of the mortgage payments over 25 years, so we can set Pmt equal to the monthly mortgage payment, r equal to the monthly interest rate, and n equal to the total number of months in 25 years.
First, let's convert the annual interest rate to a monthly interest rate by dividing by 12:
r = 7% / 12 = 0.00583
Next, we can use an online mortgage calculator or a spreadsheet to find the monthly mortgage payment based on the loan amount, interest rate, and term. For a $65,000 mortgage at 7% for 25 years, the monthly payment is approximately $471.78.
Finally, we can plug in the values into the formula for the future value of an annuity:
FV = $471.78 x ((1 + 0.00583)^300 - 1) / 0.00583
FV ≈ $141,535.15
Therefore, the total cost of the mortgage over 25 years is approximately $141,535.15. This includes the original loan amount of $65,000 plus the interest that accumulates over the 25-year period.
Explanation:
To calculate the cost of the mortgage, we need to find the total amount that Sonya will pay back over the 25-year period.
One way to do this is to use the formula for the future value of an annuity, which is:
FV = Pmt x ((1 + r)^n - 1) / r
where FV is the future value, Pmt is the periodic payment, r is the interest rate per period, and n is the number of periods. In this case, we want to find the total future value of the mortgage payments over 25 years, so we can set Pmt equal to the monthly mortgage payment, r equal to the monthly interest rate, and n equal to the total number of months in 25 years.
First, let's convert the annual interest rate to a monthly interest rate by dividing by 12:
r = 7% / 12 = 0.00583
Next, we can use an online mortgage calculator or a spreadsheet to find the monthly mortgage payment based on the loan amount, interest rate, and term. For a $65,000 mortgage at 7% for 25 years, the monthly payment is approximately $471.78.
Finally, we can plug in the values into the formula for the future value of an annuity:
FV = $471.78 x ((1 + 0.00583)^300 - 1) / 0.00583
FV ≈ $141,535.15
Therefore, the total cost of the mortgage over 25 years is approximately $141,535.15. This includes the original loan amount of $65,000 plus the interest that accumulates over the 25-year period.