Final answer:
To compute the interest paid on a 30-year mortgage with a principal amount of $370,746 and an annual interest rate of 4.7%, the total payments can be calculated using the future value formula. Subsequently, the interest paid can be found by subtracting the principal amount from the total payments. Interest paid = $647,514.57 - $370,746 = $276,768.57
Step-by-step explanation:
To compute the interest paid on a 30-year mortgage, we can use the formula:
Interest paid = Total payments - Principal amount
In this case, the principal amount is $370,746 and the annual interest rate is 4.7%. To calculate the total payments, we can use the formula for the future value of an ordinary annuity:
Future value = Payment amount × ((1 + Interest rate)^Number of periods - 1) / Interest rate
Substituting the given values, we have: Future value = $1798.65 × ((1 + 0.047)^360 - 1) / 0.047
We can solve this equation to find the future value, which is $647,514.57.
Finally, we can calculate the interest paid by subtracting the principal amount from the total payments:
Interest paid = $647,514.57 - $370,746 = $276,768.57