Mathematics of FinanceMCQPYQ 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 cRs. 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

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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)t1]CI = P\left[\left(1 + \frac{r}{100}\right)^t - 1\right] 102=P[(1+0.04)21]102 = P\left[\left(1 + 0.04\right)^2 - 1\right] 102=P[(1.04)21]102 = P\left[(1.04)^2 - 1\right] 102=P[1.08161]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.

About This Chapter: Mathematics of Finance

Paper

Paper 3: Quantitative Aptitude

Weightage

12-16 Marks

Key Topics

Simple & Compound Interest, Annuity, Perpetuity

The most important mathematical chapter in the entire syllabus. It covers Simple Interest (SI), Compound Interest (CI), Nominal vs Effective rates, Present and Future Value, Annuities (Ordinary and Due), Sinking Funds, and Perpetuities. The concepts learned here are applied heavily in CA Intermediate and Final.

View Official ICAI Syllabus

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Guaranteed 12-16 marks. Master your calculator! Learn the 'GT' and compound interest M+/M- tricks to solve annuity questions in 10 seconds without writing long formulas.

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