A trader deposited \text{₦}40,000 in a microfinance bank offering compound interest at the… — JAMB UTME

A trader deposited $\text{₦}40,000$ in a microfinance bank offering compound interest at the rate of $10\%$ per annum, compounded annually. What is the total interest earned by the trader at the end of $2$ years?

A
$\text{₦}8,000$
$\text{₦}8,400$ Answer
C
$\text{₦}40,400$
D
$\text{₦}48,400$

Answer

The total interest earned by the trader at the end of

2

years is

\text{₦}8,400

Using the compound interest formula

A = P(1 + r)^n

, the total accumulated amount after 2 years is

40,000 \times (1.1)^2 = \text{₦}48,400

. Subtracting the original principal of

\text{₦}40,000

gives the compound interest earned:

48,400 - 40,000 = \text{₦}8,400

Step-by-Step Solution

Calculate the total accumulated amount (

A

) using the compound interest formula

A = P\left(1 + \frac{R}{100}\right)^n

A = 40,000\left(1 + \frac{10}{100}\right)^2 = 40,000 \times (1.1)^2 = 40,000 \times 1.21 = \text{₦}48,400

The compound interest formula yields the total value of the investment after 2 years.

Subtract the initial principal (

P

) from the total accumulated amount (

A

) to find the compound interest (

I

I = A - P = 48,400 - 40,000 = \text{₦}8,400

Interest earned is the difference between total final amount and initial principal.

Key Concept

Calculation of compound interest vs total accumulated amount

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