A boutique owner in Enugu borrowed \text{₦}80,000 to expand her business at an annual inte… — JAMB UTME

A boutique owner in Enugu borrowed $\text{₦}80,000$ to expand her business at an annual interest rate of $15\%$ , compounded annually. If she repays the loan in full after $2$ years, what is the total interest she paid on the loan?

A
$\text{₦}24,000$
$\text{₦}25,800$ Answer
C
$\text{₦}27,600$
D
$\text{₦}105,800$

Answer

The total interest paid on the loan after 2 years is

\text{₦}25,800

The compound interest is calculated year by year. In the first year, the interest paid is

15\%

\text{₦}80,000 = \text{₦}12,000

, raising the balance to

\text{₦}92,000

. In the second year, the interest paid is

15\%

\text{₦}92,000 = \text{₦}13,800

. Adding the two yearly interest payments gives

\text{₦}12,000 + \text{₦}13,800 = \text{₦}25,800

Step-by-Step Solution

Calculate the interest for the first year.

Interest for Year 1 =

15\%

\text{₦}80,000 = \frac{15}{100} \times 80,000 = \text{₦}12,000

In compound interest, interest for the first period is calculated on the initial principal.

Determine the amount at the end of the first year, which becomes the principal for the second year.

Principal for Year 2 =

\text{₦}80,000 + \text{₦}12,000 = \text{₦}92,000

Compound interest adds earned interest to the principal for subsequent period calculations.

Calculate the interest for the second year.

Interest for Year 2 =

15\%

\text{₦}92,000 = \frac{15}{100} \times 92,000 = \text{₦}13,800

Interest in year 2 is computed on the updated principal balance of

\text{₦}92,000

Sum the interest amounts from both years to find total interest paid.

Total Interest =

\text{₦}12,000 + \text{₦}13,800 = \text{₦}25,800

The total interest is the sum of interest accumulated across each compounding period.

Key Concept

Compound Interest Calculation

Estimated Time:1m 30s

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