Mathematics for FinancePYQ Jun 24Question 1474 of 512
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Find the future value of an annuity of 5,000\displaystyle 5,000 made annually for 6\displaystyle 6 years at rate of 12%\displaystyle 12\% compounded annually, if (1+0.12)6=1.9738\displaystyle (1+0.12)^6 = 1.9738

Options

A45,575\displaystyle 45,575
B40,575\displaystyle 40,575
C39,465\displaystyle 39,465
D37,828\displaystyle 37,828
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Correct Answer

✅ Option c — 39,465\displaystyle 39,465

All Options:

  • A45,575\displaystyle 45,575
  • B40,575\displaystyle 40,575
  • C39,465\displaystyle 39,465
  • D37,828\displaystyle 37,828

Detailed Solution & Explanation

Let the principal be P\displaystyle P and the compound interest be CI\displaystyle CI. The ratio of the principal to the compound interest for 3\displaystyle 3 years (compounded annually) is given as: PCI=216127\frac{P}{CI} = \frac{216}{127} Let P=216x\displaystyle P = 216x and CI=127x\displaystyle CI = 127x. The total amount A\displaystyle A is: A=P+CI=216x+127x=343xA = P + CI = 216x + 127x = 343x The formula for compound interest amount is: A=P(1+i)3A = P(1+i)^3 where i\displaystyle i is the annual rate of interest. Substituting the values: 343x=216x(1+i)3343x = 216x(1+i)^3 (1+i)3=343216(1+i)^3 = \frac{343}{216} (1+i)3=(76)3(1+i)^3 = \left(\frac{7}{6}\right)^3 Taking the cube root on both sides: 1+i=761+i = \frac{7}{6} i=76−1=16≈0.1666 or 16.66%i = \frac{7}{6} - 1 = \frac{1}{6} \approx 0.1666 \text{ or } 16.66\% Thus, the rate of interest is approximately 0.1666\displaystyle 0.1666. Hence, **Option C** is the correct answer.

Key Concepts to Understand

Annuity

A sequence of equal periodic payments made at equal intervals of time.

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