Final answer:
To find the monthly payment for the company's 8-year term loan of $3,600,000 at an annual interest rate of 5.7%, an annuity payment formula is used. Once the monthly payment is determined, the total interest paid can be calculated by multiplying the monthly payment by the number of payments (96) and subtracting the original loan amount.
Step-by-step explanation:
To calculate the monthly payment for a $3,600,000 loan with an annual interest rate of 5.7% over an 8-year term, we use the formula for the payment of an annuity. Since payments are made monthly, we first convert the annual interest rate to a monthly rate by dividing by 12, and the total number of payments to be made over the 8 years is 8 * 12 (or 96 monthly payments).
The annuity payment formula is:
PV = R * [(1 - (1 + i)^(-n)) / i]
where:
- PV is the present value of the loan (the amount borrowed),
- R is the regular payment,
- i is the monthly interest rate, and
- n is the total number of payments.
To solve for R, we rearrange the formula to:
R = PV / [(1 - (1 + i)^(-n)) / i]
Substituting the given values, we have:
i = 5.7% / 12 = 0.00475 monthly
n = 8 * 12 = 96
PV = $3,600,000
Therefore, the monthly payment calculation is:
R = $3,600,000 / [(1 - (1 + 0.00475)^(-96)) / 0.00475]
After calculating R, we will know the monthly payment. To find the total interest paid over the life of the loan, we will multiply the monthly payment by the total number of payments (96) and subtract the principal amount ($3,600,000) from the total paid.