An investor deposited \text{₦}60,000 into a financial scheme for 2 years at an annual inte… — JAMB UTME

An investor deposited $\text{₦}60,000$ into a financial scheme for $2$ years at an annual interest rate of $r\%$ . If the difference between the compound interest (compounded annually) and the simple interest earned over the $2$ -year period is $\text{₦}384$ , calculate the value of $r$ .

Cevap: 8 %

Cevap

The interest rate r is 8%

For a two-year investment period, the difference between compound interest (compounded annually) and simple interest equals the interest earned in the second year on the first year's interest, which is

P \left(\frac{r}{100}\right)^2

. Setting

60,000 \times \frac{r^2}{10,000} = 384

yields

6r^2 = 384

, giving

r^2 = 64

and

r = 8\%

Adım Adım Çözüm

Express the simple interest for 2 years in terms of r

I_{\text{SI}} = 1,200r

Simple interest is calculated directly on the principal amount for the full term.

Express the compound interest for 2 years in terms of r

I_{\text{CI}} = 1,200r + 6r^2

Compound interest includes interest earned on the first year's interest.

Set up the equation for the difference between compound and simple interest

(1,200r + 6r^2) - 1,200r = 384 \implies 6r^2 = 384

The difference between CI and SI over 2 years isolates the interest-on-interest component.

Solve for r

r = 8

Dividing 384 by 6 gives 64, and taking the principal square root yields 8.

Anahtar Kavram

Difference between Compound Interest and Simple Interest for 2 years

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