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

A poultry farmer in Ogun State took a loan of ₦120,000\text{₦}120,000 from a cooperative society at an annual interest rate of 5%5\%, compounded annually. What is the total interest paid by the farmer at the end of 22 years?

  1. ₦12,300\text{₦}12,300Answer
  2. B
    ₦132,300\text{₦}132,300
  3. C
    ₦12,000\text{₦}12,000
  4. D
    ₦132,000\text{₦}132,000

Answer

The total compound interest paid at the end of 2 years is ₦12,300\text{₦}12,300.
The total compound interest is determined by calculating the accumulated amount A=120,000×(1.05)2=₦132,300A = 120,000 \times (1.05)^2 = \text{₦}132,300 and subtracting the original principal of ₦120,000\text{₦}120,000, yielding ₦12,300\text{₦}12,300.

Step-by-Step Solution

1
Identify the given values for principal, rate, and time
Principal P=₦120,000P = \text{₦}120,000, Rate r=5%=0.05r = 5\% = 0.05, Time t=2 yearst = 2\text{ years}
These parameters are required to substitute into the compound amount formula.
2
Calculate the total accumulated amount AA after 2 years
A=P(1+r)t=120,000×(1+0.05)2=120,000×1.1025=₦132,300A = P(1 + r)^t = 120,000 \times (1 + 0.05)^2 = 120,000 \times 1.1025 = \text{₦}132,300
The compound interest formula yields the total balance including the initial principal.
3
Subtract the initial principal from the total accumulated amount to determine interest
Compound Interest =A−P=132,300−120,000=₦12,300= A - P = 132,300 - 120,000 = \text{₦}12,300
Interest is the extra amount generated beyond the original loan amount.

Key Concept

Compound Interest vs Total Accumulated Amount
Estimated Time:1m 30s
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Topics

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

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