Final answer:
The required year-end payments for a three-year $10,000 loan at an 8% interest rate is $3,880.34 per year.
Step-by-step explanation:
To determine the required year-end payments for a three-year $10,000 loan with an 8% annual interest rate, we need to use the formula for the annuity payment. The formula takes into account the present value of the loan, the interest rate, and the number of periods. In this case, since the interest is compounded annually, the formula to find the annuity payment (A) is:
A = P * (r(1+r)^n) / ((1+r)^n - 1)
Where:
- P is the principal amount ($10,000)
- r is the annual interest rate (8% or 0.08)
- n is the number of periods (3 years)
Plugging in the values, we can calculate the annuity payment as:
A = $10,000 * (0.08(1+0.08)^3) / ((1+0.08)^3 - 1) = $3,880.34
Therefore, the required year-end payment for the loan is $3,880.34, which corresponds to option b.