Question

A certain college graduate borrows 5347 dollars to buy a car. The lender charges interest at an annual rate of 10%. Assuming that interest is compounded continuously and that the borrower makes payments continuously at a constant annual rate k dollars per year. determine the payment rate that is required to pay off the loan in 3 years. Also determine how much interest is paid during the 3 -year period. Round your answers to two decimal places. Payment rate = dollars per year Interest paid = dollars

Answer 1

The payment rate (k) required to pay off a loan of 5347 dollars over 3 years with a 10% interest rate compounded continuously can be calculated using a formula involving the present value, interest rate, and time. The total interest paid is the difference between the initial loan and total amount paid over the loan period.

Step-by-step explanation:

The question asks to determine the payment rate required to pay off a loan of 5347 dollars in 3 years with a 10% annual interest rate compounded continuously, and the total interest paid over the three-year period. To calculate the payment rate (k), we use the formula for continuous compounding and repayment:

PV = k/er - k/(ert - 1), where PV is the present value of the loan, r is the annual interest rate, and t is the time in years.

By rearranging and solving for k, we can find the required annual payment rate. After determining k, we can calculate the total amount of interest paid by subtracting the initial loan amount from the total payments made over 3 years.