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Difficulty: MediumFinancial Mathematics (Interest, Profit, Loss, and Depreciation)

A business owner borrowed ₦150,000\text{₦}150,000 to expand his store at a compound interest rate of 8%8\% per annum, compounded annually. What is the total compound interest he will pay at the end of 2 years?

  1. ₦24,960\text{₦}24,960Answer
  2. B
    ₦174,960\text{₦}174,960
  3. C
    ₦24,000\text{₦}24,000
  4. D
    ₦26,960\text{₦}26,960

Answer

The total compound interest paid at the end of 2 years is ₦24,960\text{₦}24,960.
The total compound interest is obtained by calculating the interest accrued in each period (12,00012,000 in Year 1 and 12,96012,960 in Year 2) and summing them to get ₦24,960\text{₦}24,960. Alternatively, using the compound interest formula I=P(1+r)n−PI = P(1 + r)^n - P, I=150,000(1.08)2−150,000=174,960−150,000=₦24,960I = 150,000(1.08)^2 - 150,000 = 174,960 - 150,000 = \text{₦}24,960.

Step-by-Step Solution

1
Calculate the interest for the first year.
Interest1=8100×150,000=₦12,000\text{Interest}_1 = \frac{8}{100} \times 150,000 = \text{₦}12,000
Interest in the first year is calculated on the initial principal.
2
Find the principal for the second year.
Principal2=150,000+12,000=₦162,000\text{Principal}_2 = 150,000 + 12,000 = \text{₦}162,000
Under compound interest, the first year's interest is added to the initial principal.
3
Calculate the interest for the second year.
Interest2=8100×162,000=₦12,960\text{Interest}_2 = \frac{8}{100} \times 162,000 = \text{₦}12,960
Interest in the second year is calculated on the updated principal.
4
Sum the interest from both years to find the total compound interest.
Total Interest=12,000+12,960=₦24,960\text{Total Interest} = 12,000 + 12,960 = \text{₦}24,960
The total compound interest is the sum of interest accumulated in each compounding period.

Key Concept

Compound Interest
Estimated Time:1m 30s
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Topics

Financial Mathematics (Interest, Profit, Loss, and Depreciation)

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