Final answer:
To calculate the total interest paid on a loan, one would typically use the present value of an annuity formula. However, without knowing the principal amount of the loan, we cannot provide a precise answer. An amortization schedule or financial calculator can help determine the sum of interest paid across all payments.
Step-by-step explanation:
To calculate the total interest paid on a loan with monthly payments, we must understand the process of amortization for an installment loan. In the case provided, a loan is repaid with end-of-month payments of $450 over seven years, with an interest rate of 12% compounded monthly. The formula for the monthly payment on an amortizing loan is derived from the present value of an annuity formula:
PV = R [1 - (1 + i)^-n] / i
Where:
- PV is the present value of the loan (initial loan amount),
- R is the monthly payment,
- i is the monthly interest rate,
- n is the total number of payments.
However, in this situation, we are not given the initial loan amount; instead, we are asked to determine the total interest paid over the life of the loan. This requires a different approach that often involves constructing an amortization schedule or utilizing a financial calculator to determine the sum of interest paid across all payments.
The total interest paid can be calculated by taking the total of all payments made over the seven years and subtracting the original loan amount (which we would have calculated using the monthly payment, rate, and number of payments). Unfortunately, without the original loan amount, we cannot provide a precise answer to how much interest was paid. To solve this, we would need additional information, such as the principal amount of the loan.