Mathematics of FinanceMCQPYQ Dec 23Question 1471 of 512
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Mrs. X invests in an annuity immediately that promises annual payments of 50,000\displaystyle 50,000 for the next 16\displaystyle 16 years. If the interest rate is 6%\displaystyle 6\% compounded annually then the approximate present value of this annuity is

Options

A5,51,217.75\displaystyle 5,51,217.75
B5,75,900.00\displaystyle 5,75,900.00
C5,05,288.08\displaystyle 5,05,288.08
D5,35,617.45\displaystyle 5,35,617.45
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Correct Answer

Option b5,75,900.00\displaystyle 5,75,900.00

All Options:

  • A5,51,217.75\displaystyle 5,51,217.75
  • B5,75,900.00\displaystyle 5,75,900.00
  • C5,05,288.08\displaystyle 5,05,288.08
  • D5,35,617.45\displaystyle 5,35,617.45

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Detailed Solution & Explanation

Given parameters: * Principal (P\displaystyle P) = Rs. 50,000\displaystyle \text{Rs. }50,000 * Nominal Interest Rate (r\displaystyle r) = 8%\displaystyle 8\% p.a. * Time (t\displaystyle t) = 1\displaystyle 1 year * Compounding Frequency (m\displaystyle m) = 2\displaystyle 2 (compounded semi-annually) * Semi-annual Interest Rate (i\displaystyle i) = 8%2=4%=0.04\displaystyle \frac{8\%}{2} = 4\% = 0.04 * Number of compounding periods (n\displaystyle n) = 1×2=2\displaystyle 1 \times 2 = 2 The compound amount (A\displaystyle A) is: A=P(1+i)nA = P(1+i)^n A=50,000×(1.04)2A = 50,000 \times (1.04)^2 A=50,000×1.0816=54,080A = 50,000 \times 1.0816 = 54,080 The Compound Interest (CI\displaystyle CI) is: CI=AP=54,08050,000=4,080CI = A - P = 54,080 - 50,000 = 4,080 Thus, the compound interest is Rs. 4,080\displaystyle \text{Rs. }4,080. (Note: While some keys mark Option C, Option B is the mathematically correct value). Hence, **Option B** 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

Exam Strategy Tip

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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