Final answer:
The annual payment on a $20,000 loan at 10% interest with annual compounding over a 5-year term is approximately $5,275.95, closest to option c.
Step-by-step explanation:
To determine the annual payment for a $20,000 loan with a 5-year term and a 10% interest rate (compounded annually), we can use the formula for the annuity payment from present value (PV). The formula is:
A = PV * [r(1+r)^n] / [(1+r)^n - 1]
Where:
- A = annuity payment (what we are solving for)
- PV = present value of the loan ($20,000)
- r = annual interest rate (0.10)
- n = number of periods (5 years)
Plugging in the values:
A = $20,000 * [0.10(1+0.10)^5] / [(1+0.10)^5 - 1]
A = $20,000 * [0.10(1.10)^5] / [(1.10)^5 - 1]
A = $20,000 * [0.10 * 1.61051] / [1.61051 - 1]
A = $20,000 * 0.161051 / 0.61051
A = $20,000 * 0.263797
A = $5,275.94
The closest answer to this calculation is c. $5,275.95. Therefore, the annual payment on a $20,000 loan at 10% interest, compounded annually over 5 years, is approximately $5,275.95.