What principal would amount to ₹21,420 in 2 years at the rate of 9.5% p.a. simple interest?

Question

What principal would amount to ₹21,420 in 2 years at the rate of 9.5% p.a. simple interest?

1. A. ₹16,000
2. B. ₹12,000
3. C. ₹11,273
4. D. ₹18,000 (Correct answer)

Correct Answer

Option D — ₹18,000

Detailed Solution & Explanation

The correct answer is ₹18,000.

Key Points

• Amount $=P\left(1+\dfrac{RT}{100}\right)=P\left(1+\dfrac{9.5\times2}{100}\right)=P\cdot\dfrac{119}{100}$.
• $21420=\dfrac{119P}{100}\Rightarrow P=\dfrac{21420\times100}{119}=18000$.

Additional Information

• For simple interest the amount is A = P(1 + RT/100), so the principal is recovered by dividing rather than by subtracting interest.
• Working the fraction exactly (119/100) avoids the rounding that creeps in if the interest is computed first.
• Contrast compound interest, where A = P(1 + R/100)ᵀ; at the same rate and time it always exceeds the simple-interest amount.