Mathematics of FinanceMCQPYQ Sep 24Question 1481 of 512
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In an account paying interest @9%\displaystyle @9\% per year compounded monthly, 200\displaystyle 200 is invested at the end of each month. What is the future value of this annuity after 10th\displaystyle 10^{th} payment? (Where (1.00/5)10=1.0775\displaystyle (1.00/5)^{10} = 1.0775 )

Options

A2,060\displaystyle 2,060
B2,022\displaystyle 2,022
C2,044\displaystyle 2,044
D2,155\displaystyle 2,155
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Correct Answer

Option a2,060\displaystyle 2,060

All Options:

  • A2,060\displaystyle 2,060
  • B2,022\displaystyle 2,022
  • C2,044\displaystyle 2,044
  • D2,155\displaystyle 2,155

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Detailed Solution & Explanation

The future value (FV\displaystyle FV) of an ordinary annuity is: FV=A[(1+i)n1i]FV = A \left[ \frac{(1+i)^n - 1}{i} \right] Given: * Monthly payment (A\displaystyle A) = 200\displaystyle 200 * Nominal interest rate (r\displaystyle r) = 9%\displaystyle 9\% p.a. * Compounding frequency (m\displaystyle m) = 12\displaystyle 12 (monthly), so periodic interest rate i=9%12=0.75%=0.0075\displaystyle i = \frac{9\%}{12} = 0.75\% = 0.0075 * Number of payments (n\displaystyle n) = 10\displaystyle 10 * Given factor: (1.0075)10=1.0775\displaystyle (1.0075)^{10} = 1.0775 Substituting the values: FV=200[1.077510.0075]=200×0.07750.00752066.67FV = 200 \left[ \frac{1.0775 - 1}{0.0075} \right] = 200 \times \frac{0.0775}{0.0075} \approx 2066.67 The calculated future value is approximately 2,066.67\displaystyle 2,066.67, which is closest to Option A (2,060\displaystyle 2,060 in system records). 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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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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