Mathematics for FinancePYQ Nov 18Question 1184 of 512
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If compound interest on a sum for 2\displaystyle 2 years at 4%\displaystyle 4\% per annum is Rs. 102\displaystyle \text{Rs. }102, then the simple interest on the same sum for the same period at the same rate will be

Options

ARs. 99\displaystyle \text{Rs. }99
BRs. 101\displaystyle \text{Rs. }101
CRs. 100\displaystyle \text{Rs. }100
DRs. 95\displaystyle \text{Rs. }95
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Correct Answer

✅ Option c — Rs. 100\displaystyle \text{Rs. }100

All Options:

  • ARs. 99\displaystyle \text{Rs. }99
  • BRs. 101\displaystyle \text{Rs. }101
  • CRs. 100\displaystyle \text{Rs. }100
  • DRs. 95\displaystyle \text{Rs. }95

Detailed Solution & Explanation

**Derivation of Simple Interest from Compound Interest** Given: - Compound Interest (CI\displaystyle CI) = Rs. 102\displaystyle \text{Rs. }102 - Time (t\displaystyle t) = 2\displaystyle 2 years - Rate of Interest (r\displaystyle r) = 4%\displaystyle 4\% per annum **Step 1: Find the Principal (P\displaystyle P) using Compound Interest** CI=P[(1+r100)t−1]CI = P\left[\left(1 + \frac{r}{100}\right)^t - 1\right] 102=P[(1+0.04)2−1]102 = P\left[\left(1 + 0.04\right)^2 - 1\right] 102=P[(1.04)2−1]102 = P\left[(1.04)^2 - 1\right] 102=P[1.0816−1]102 = P[1.0816 - 1] 102=0.0816P102 = 0.0816 P P=1020.0816=Rs. 1,250P = \frac{102}{0.0816} = \text{Rs. }1,250 **Step 2: Calculate the Simple Interest (SI\displaystyle SI) for the same Principal, Rate, and Time** SI=P×r×t100SI = \frac{P \times r \times t}{100} SI=1250×4×2100SI = \frac{1250 \times 4 \times 2}{100} SI=10000100=Rs. 100SI = \frac{10000}{100} = \text{Rs. }100 Hence, **Option C** is the correct answer.

Key Concepts to Understand

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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If Rs. 1,000\displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every 10\displaystyle 10 years, then the number in years in which it will amount to Rs. 2,000\displaystyle \text{Rs. }2,000 is:

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