If the simple interest on a sum of money invested at 3% per annum for 2$\frac{1}{2}$  years is N123, find the principal.

Analysis

To solve this problem, we need to use the standard formula for Simple Interest. We are given the interest rate, the time, and the total interest earned, and we are asked to find the principal amount that was invested.

Concept

The formula for Simple Interest ($I$) is:

Where:

• $I$ = Simple Interest (N123)
• $P$ = Principal (the amount we need to find)
• $R$ = Rate per annum (3%)
• $T$ = Time in years ($2\frac{1}{2}$ years, which is 2.5 years)

Step-by-Step Solution

Step 1: Rearrange the formula to make $P$ the subject. Since $I = \frac{P \times R \times T}{100}$, we can multiply both sides by 100 and divide by $(R \times T)$:

Step 2: Substitute the given values into the formula.

• $I = 123$
• $R = 3$
• $T = 2.5$

Step 3: Perform the calculation.

• First, calculate the denominator: $3 \times 2.5 = 7.5$
• Now, divide the numerator by the denominator:

To make the division easier, multiply both numerator and denominator by 10:

Dividing 123,000 by 75: $123000 \div 75 = 1640$

The Principal is N1,640.

Conclusion

Comparing our result to the given options, we find that it matches option C.

Exam Tip

When dealing with mixed fractions like $2\frac{1}{2}$ in interest calculations, always convert them to decimals (2.5) or improper fractions ($\frac{5}{2}$) before plugging them into your formula. This prevents errors during multiplication. Also, remember that "per annum" simply means "per year," so ensure your time ($T$) is always in years!