Question

A bank just approved your small business loan for $20,000. The loan has an interest rate of 8% and will be repaid with 10 end-of-year payments.

1) What is the required annual loan payment?
a) $4,572.23
b) $4,373.14
c) $2,980.59
d) $4,456.43
e) $3,254.91

Answer 1

The required annual loan payment for a $20,000 loan with an 8% interest rate and 10 end-of-year payments is $2,980.59.

Step-by-step explanation:

To find the required annual loan payment, we can use the formula for the present value of an annuity: PV = PMT × (1 - (1 + r)^-n) / r, where PV is the loan amount ($20,000), PMT is the required annual loan payment, r is the interest rate (8% or 0.08), and n is the number of payments (10). By plugging in these values, we can solve for PMT:

PMT × (1 - (1 + 0.08)^-10) / 0.08 = $20,000

PMT × (1 - 1.08^-10) / 0.08 = $20,000

PMT × (1 - 0.463193) / 0.08 = $20,000

PMT × 0.536807 / 0.08 = $20,000

PMT × 6.7100875 = $20,000

PMT = $20,000 / 6.7100875

PMT = $2,980.59

Therefore, the required annual loan payment is $2,980.59. So, option c) $2,980.59 is the correct answer.