Mathematics of FinanceMCQPYQ Dec 23Question 1468 of 512
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How much amount is required to be invested every year so as to accumulate 50,000\displaystyle 50,000 at the end of 10\displaystyle 10 years, if the interest compounded annually at 10%\displaystyle 10\%. Given A(10,0.1)=15.9374\displaystyle A(10, 0.1) = 15.9374

Options

A1882.36\displaystyle 1882.36
B1828.30\displaystyle 1828.30
C1832.65\displaystyle 1832.65
D1853.65\displaystyle 1853.65
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Correct Answer

Option a1882.36\displaystyle 1882.36

All Options:

  • A1882.36\displaystyle 1882.36
  • B1828.30\displaystyle 1828.30
  • C1832.65\displaystyle 1832.65
  • D1853.65\displaystyle 1853.65

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Detailed Solution & Explanation

Let the principal be P\displaystyle P. Given parameters: * Compound Interest (CI\displaystyle CI) = Rs. 3,280\displaystyle \text{Rs. }3,280 * Rate of interest (r\displaystyle r) = 5%\displaystyle 5\% p.a., so i=0.05\displaystyle i = 0.05 * Time (t\displaystyle t) = 2\displaystyle 2 years The formula for Compound Interest compounded annually is: CI=P[(1+i)t1]CI = P\left[(1+i)^t - 1\right] Substituting the values: 3,280=P[(1.05)21]3,280 = P\left[(1.05)^2 - 1\right] 3,280=P[1.10251]3,280 = P[1.1025 - 1] 3,280=0.1025P3,280 = 0.1025P Solving for P\displaystyle P: P=3,2800.1025=32,000P = \frac{3,280}{0.1025} = 32,000 Thus, the principal sum is Rs. 32,000\displaystyle \text{Rs. }32,000. (Note: While some keys mark Option C, the mathematically correct value is Option A). 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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