Mathematics of FinanceMCQMTP Dec 23 Series IIQuestion 1430 of 512
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If the Compound Interest on a certain sum of money for 2 years at 4%\displaystyle 4\% p.a. be 510\displaystyle 510, then its simple Interest (S.I.) of same time at same rate of interest is

Options

A500\displaystyle 500
B510\displaystyle 510
C450\displaystyle 450
DNone of these
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Correct Answer

Option a500\displaystyle 500

All Options:

  • A500\displaystyle 500
  • B510\displaystyle 510
  • C450\displaystyle 450
  • DNone of these

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Detailed Solution & Explanation

Let the principal be P\displaystyle P. The rate of interest is r=4%\displaystyle r = 4\% p.a., so i=0.04\displaystyle i = 0.04. The time period is t=2\displaystyle t = 2 years. The Compound Interest (CI\displaystyle CI) is given by: CI=P[(1+i)t1]CI = P\left[(1+i)^t - 1\right] Substituting the values: 510=P[(1.04)21]510 = P\left[(1.04)^2 - 1\right] 510=P[1.08161]510 = P[1.0816 - 1] 510=0.0816P510 = 0.0816P Solving for P\displaystyle P: P=5100.0816=6,250P = \frac{510}{0.0816} = 6,250 The Simple Interest (SI\displaystyle SI) on the same principal for the same period at the same rate is: SI=P×r×t100SI = \frac{P \times r \times t}{100} SI=6,250×4×2100=500SI = \frac{6,250 \times 4 \times 2}{100} = 500 Thus, the simple interest is Rs. 500\displaystyle \text{Rs. }500. Hence, **Option A** 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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