Find the principal which amounts to ₦ 5,500 at a simple interest in 5 years at 2% per annum

Analysis

To solve this problem, we need to understand the relationship between the Principal ($P$), the Amount ($A$), the Rate ($R$), and the Time ($T$) under simple interest.

Concept

In simple interest, the Amount ($A$) is the sum of the Principal ($P$) and the Simple Interest ($I$).

1. The formula for Simple Interest is: $I = \frac{P \times R \times T}{100}$
2. The formula for Amount is: $A = P + I$
3. Substituting the interest formula into the amount formula gives: $A = P + \frac{PRT}{100}$
4. We can factor out $P$: $A = P(1 + \frac{RT}{100})$

Solution

Given:

• Amount ($A$) = ₦ 5,500
• Time ($T$) = 5 years
• Rate ($R$) = 2%
• Principal ($P$) = ?

Using the formula $A = P(1 + \frac{RT}{100})$:

$5500 = P(1 + \frac{2 \times 5}{100})$

$5500 = P(1 + \frac{10}{100})$

$5500 = P(1 + 0.1)$

$5500 = P(1.1)$

Now, solve for $P$: $P = \frac{5500}{1.1}$

$P = \frac{55000}{11}$

$P = 5000$

The principal is ₦ 5,000.

Conclusion

Comparing our result with the given options, the correct choice is B.

Exam Tip

When dealing with simple interest questions, always check if the question asks for the "Interest" or the "Amount." If it asks for the "Amount," remember that you must add the interest back to the principal. A common mistake is to calculate only the interest and stop there!