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If a student borrows $20,000 to start a business as a 5 year, 10% loan (with annual compounding), the annual payment is:

a. $3,275.95
b. $2,000.00
c. $5,275.95
d. $4,000.00

User Albz
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1 Answer

2 votes

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.

User Antik
by
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