Mathematics of FinanceMCQMTP Dec 23 Series IIQuestion 1528 of 512
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Find the future value of an annuity of 500\displaystyle 500 is made annually for 7\displaystyle 7 years at interest rate of 14%\displaystyle 14\% compounded annually. [(1.14)7=2.5023]\displaystyle [(1.14)^7 = 2.5023]

Options

A5365.25\displaystyle 5365.25
B5265.25\displaystyle 5265.25
C5465.25\displaystyle 5465.25
DNone of these
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Correct Answer

Option a5365.25\displaystyle 5365.25

All Options:

  • A5365.25\displaystyle 5365.25
  • B5265.25\displaystyle 5265.25
  • C5465.25\displaystyle 5465.25
  • DNone of these

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Detailed Solution & Explanation

The future value (FV\displaystyle FV) of the annuity is: FV=A[(1+i)n1i]FV = A \left[ \frac{(1+i)^n - 1}{i} \right] Given: * Annual investment (A\displaystyle A) = 500\displaystyle 500 * Time (n\displaystyle n) = 7\displaystyle 7 years * Interest rate (i\displaystyle i) = 14%\displaystyle 14\% p.a. = 0.14\displaystyle 0.14 * Given factor (1.14)7=2.5023\displaystyle (1.14)^7 = 2.5023 Substituting the values: FV=500[2.502310.14]5,365.36FV = 500 \left[ \frac{2.5023 - 1}{0.14} \right] \approx 5,365.36 This is closest to Option A (5365.25\displaystyle 5365.25). 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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