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

A cooperative society in Akure granted a loan of ₦160,000\text{₦}160,000 to a farmer at an interest rate of 12%12\% per annum, compounded annually. What is the total compound interest owed at the end of 22 years?

  1. ₦40,704\text{₦}40,704Answer
  2. B
    ₦200,704\text{₦}200,704
  3. C
    ₦38,400\text{₦}38,400
  4. D
    ₦19,200\text{₦}19,200

Answer

The total compound interest owed at the end of 2 years is ₦40,704\text{₦}40,704.
The compound interest is obtained by calculating the accumulated amount A=160,000×(1.12)2=₦200,704A = 160,000 \times (1.12)^2 = \text{₦}200,704 and then subtracting the principal of ₦160,000\text{₦}160,000 to get ₦40,704\text{₦}40,704.

Step-by-Step Solution

1
Identify the given financial variables
Principal P=₦160,000P = \text{₦}160,000, Rate R=12%R = 12\%, Time n=2n = 2 years.
Establishing the parameters needed for the compound interest formula.
2
Calculate the total accumulated amount AA using the formula A=P(1+R100)nA = P\left(1 + \frac{R}{100}\right)^n
A=160,000×(1+0.12)2=160,000×(1.12)2=160,000×1.2544=₦200,704A = 160,000 \times \left(1 + 0.12\right)^2 = 160,000 \times (1.12)^2 = 160,000 \times 1.2544 = \text{₦}200,704.
Determines the total value of the loan including principal and accrued compound interest after 2 years.
3
Subtract the principal PP from the total amount AA to find the compound interest CICI
CI=A−P=200,704−160,000=₦40,704CI = A - P = 200,704 - 160,000 = \text{₦}40,704.
Isolates the interest portion from the total accumulated balance.

Key Concept

Compound Interest Calculation
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Topics

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

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