Mathematics for FinanceMTP Jun 23 Series IQuestion 1520 of 512
All Questions

Raju invests 20,000\displaystyle 20,000 every year in a deposit scheme starting from today for next 12\displaystyle 12 years. Assuming that interest rate on his deposit is 7%\displaystyle 7\% per annum compounded annually. What will be the future value of this annuity?

Options

A540,576\displaystyle 540,576
B382,813\displaystyle 382,813
C643,483\displaystyle 643,483
D357,769\displaystyle 357,769
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — 382,813\displaystyle 382,813

All Options:

  • A540,576\displaystyle 540,576
  • B382,813\displaystyle 382,813
  • C643,483\displaystyle 643,483
  • D357,769\displaystyle 357,769

Detailed Solution & Explanation

Since payments are made starting today, this is an annuity due. The future value (FVdue\displaystyle FV_{\text{due}}) is: FVdue=A[(1+i)n−1i]×(1+i)FV_{\text{due}} = A \left[ \frac{(1+i)^n - 1}{i} \right] \times (1+i) Given: * Annual investment (A\displaystyle A) = 20,000\displaystyle 20,000 * Time (n\displaystyle n) = 12\displaystyle 12 years * Interest rate (i\displaystyle i) = 7%\displaystyle 7\% p.a. = 0.07\displaystyle 0.07 Substituting the values: Annuity factor=(1.07)12−10.07≈2.25219−10.07=17.88845\text{Annuity factor} = \frac{(1.07)^{12} - 1}{0.07} \approx \frac{2.25219 - 1}{0.07} = 17.88845 FVdue=20,000×17.88845×1.07≈3,82,812.83FV_{\text{due}} = 20,000 \times 17.88845 \times 1.07 \approx 3,82,812.83 This matches Option B (382,813\displaystyle 382,813). Hence, **Option B** is the correct answer.

Key Concepts to Understand

More Questions from Mathematics for Finance

Ready to Master Mathematics for Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free