A businesswoman invested \text{₦}50,000 in a financial fund. Part of the money was investe… — JAMB UTME

A businesswoman invested $\text{₦}50,000$ in a financial fund. Part of the money was invested at a simple interest rate of $6\%$ per annum, and the remaining part was invested at $8\%$ simple interest per annum. If the total interest earned at the end of $1$ year was $\text{₦}3,600$ , what was the amount, in Naira, invested at the $8\%$ interest rate?

Answer: 30000 Naira

Answer

The amount invested at the

8\%

interest rate is

\text{₦}30,000

Setting up the linear equation for annual simple interest gives

0.06(50,000 - x) + 0.08x = 3,600

. Simplifying this yields

3,000 + 0.02x = 3,600

, which solves to

x = 30,000

. Thus,

\text{₦}30,000

was invested at

8\%

Step-by-Step Solution

Define variables for the two investment amounts.

Let

x

be the amount in Naira invested at

8\%

, so

(50,000 - x)

is the amount invested at

6\%

The total capital of

\text{₦}50,000

is split into two distinct portions.

Formulate the total interest expression using the simple interest formula

I = \frac{P \times R \times T}{100}

\frac{6}{100}(50,000 - x) + \frac{8}{100}x = 3,600

The sum of annual interests from both parts equals the total interest earned of

\text{₦}3,600

Expand the terms and solve the linear equation for

x

3,000 + 0.02x = 3,600 \implies 0.02x = 600 \implies x = 30,000

Isolating

x

yields the exact principal amount allocated to the

8\%

interest rate.

Key Concept

Simple Interest and Allocation of Principal across Different Interest Rates

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

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