Final answer:
To find the original principal amount of a four-year loan with a 13% interest rate and annual payments of $5,043.71, one must use the present value of an annuity formula. The answer will be the one that matches the calculation using the given payments, interest rate, and loan period.
Step-by-step explanation:
The student is asking to determine the original principal amount of a loan, given that Donna makes annual end-of-year payments of $5,043.71 on a four-year loan with an interest rate of 13 percent. To solve this, we must use the formula for the present value of an annuity since the payments are made at the end of each year. The present value of an annuity formula is PV = PMT [1 - (1 + r)^-n] / r, where PV is the present value (initial loan amount), PMT is the annual payment, r is the interest rate per period, and n is the number of periods.
Plugging in the values from the question:
- PMT = $5,043.71
- r = 0.13 (13 percent annual interest rate)
- n = 4 (loan lasts for four years)
Calculating using the formula, we can find the original principal amount.