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Zorluk: OrtaFinancial Mathematics (Interest, Profit, Loss, and Depreciation)

A boutique owner in Enugu borrowed ₦80,000\text{₦}80,000 to expand her business at an annual interest rate of 15%15\%, compounded annually. If she repays the loan in full after 22 years, what is the total interest she paid on the loan?

  1. A
    ₦24,000\text{₦}24,000
  2. ₦25,800\text{₦}25,800Cevap
  3. C
    ₦27,600\text{₦}27,600
  4. D
    ₦105,800\text{₦}105,800

Cevap

The total interest paid on the loan after 2 years is ₦25,800\text{₦}25,800.
The compound interest is calculated year by year. In the first year, the interest paid is 15%15\% of ₦80,000=₦12,000\text{₦}80,000 = \text{₦}12,000, raising the balance to ₦92,000\text{₦}92,000. In the second year, the interest paid is 15%15\% of ₦92,000=₦13,800\text{₦}92,000 = \text{₦}13,800. Adding the two yearly interest payments gives ₦12,000+₦13,800=₦25,800\text{₦}12,000 + \text{₦}13,800 = \text{₦}25,800.

Adım Adım Çözüm

1
Calculate the interest for the first year.
Interest for Year 1 = 15%15\% of ₦80,000=15100×80,000=₦12,000\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.
2
Determine the amount at the end of the first year, which becomes the principal for the second year.
Principal for Year 2 = ₦80,000+₦12,000=₦92,000\text{₦}80,000 + \text{₦}12,000 = \text{₦}92,000.
Compound interest adds earned interest to the principal for subsequent period calculations.
3
Calculate the interest for the second year.
Interest for Year 2 = 15%15\% of ₦92,000=15100×92,000=₦13,800\text{₦}92,000 = \frac{15}{100} \times 92,000 = \text{₦}13,800.
Interest in year 2 is computed on the updated principal balance of ₦92,000\text{₦}92,000.
4
Sum the interest amounts from both years to find total interest paid.
Total Interest = ₦12,000+₦13,800=₦25,800\text{₦}12,000 + \text{₦}13,800 = \text{₦}25,800.
The total interest is the sum of interest accumulated across each compounding period.

Anahtar Kavram

Compound Interest Calculation
Tahmini Süre:1m 30s
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Financial Mathematics (Interest, Profit, Loss, and Depreciation)

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