Final answer:
The loan amount that is taken is $1974.71.
Step-by-step explanation:
The student is looking to determine the original loan amount for a scenario where the loan is repaid in equal annual installments, with a given interest rate and a set repayment time frame. This is a problem involving the calculation of the present value of an annuity. Since we know the amount of each installment, the interest rate, and the number of periods, we can use the formula for the present value of an annuity:
PV = Pmt * [(1 - (1 + r)^-n) / r]
To find the loan amount that is taken, we can use the formula for the present value of an annuity:
Loan Amount = Annual Payment * (1 - (1 + interest rate)^(-number of years))) / interest rate
Given that the annual payment is $318, the interest rate is 6.0%, and the number of years is 8, we can plug in these values to calculate the loan amount:
Loan Amount = 318 * (1 - (1 + 0.06)^(-8)) / 0.06 = $1974.71
Therefore, the correct answer is a. 1974.71.