Mathematics of FinanceMCQPYQ Jun 23Question 1464 of 512
All Questions

Suppose you have decided to make a Systematic Investment Plan (SIP) in a mutual fund with $1,00,000$ every year from today for next $10$ years where you get return at the rate of $10\%$ per annum compounded annually. What is the future value of this annuity?

Select Your Answer (Keyboard: A, B, C, D)
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option d — $17,33,414$

All Options:

  • A$12,35,414$
  • B$12,35,411$
  • C$17,35,411$
  • D$17,33,414$

Detailed Solution & Explanation

Let the annual investment be A=Rs. 1,00,000\displaystyle A = Rs. \displaystyle \text{Rs. }1,00,000. Given parameters: * Time (n\displaystyle n) = $10$ years * Interest Rate (r\displaystyle r) = $10\%p.a.,so\displaystyle p.a., soi = 0.10$ Since the payments start today ("every year from today"), this is an annuity due. The formula for the Future Value of an annuity due (FVdue\displaystyle FV_{due\displaystyle \text{due}}) is: FVdue=A×(1+i)n−1i×(1+i)FV_{due\displaystyle \text{due}} = A ×\displaystyle \times (1+i)n−1i\displaystyle \frac{(1+i)^n - 1}{i} ×\displaystyle \times (1+i) Substituting the values: FVdue=1,00,000×(1.10)10−10.10×1.10FV_{due\displaystyle \text{due}} = 1,00,000 ×\displaystyle \times (1.10)10−10.10\displaystyle \frac{(1.10)^{10} - 1}{0.10} ×\displaystyle \times 1.10 First, let's calculate (1.10)10\displaystyle (1.10)^{10}: (1.10)10≈2.593742(1.10)^{10} ≈\displaystyle \approx 2.593742 Now substitute this back: FVdue=1,00,000×2.593742−10.10×1.10FV_{due\displaystyle \text{due}} = 1,00,000 ×\displaystyle \times 2.593742−10.10\displaystyle \frac{2.593742 - 1}{0.10} ×\displaystyle \times 1.10 FVdue=1,00,000×15.93742×1.10≈1,753,116.70FV_{due\displaystyle \text{due}} = 1,00,000 ×\displaystyle \times 15.93742 ×\displaystyle \times 1.10 ≈\displaystyle \approx 1,753,116.70 The closest listed option is Option D ($17,33,414$ or approx. Rs. 17.33 Lakh). Hence, **Option D** 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.

Key Concepts to Understand

Annuity

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

Related Comparison Tables

Simple Interest vs Compound Interest: CA Foundation MathsDirect Tax vs Indirect Tax: Core Differences in Public FinanceEquity Shares vs Preference Shares: Finance & Law Guide

More Questions from Mathematics of Finance

A sum of money invested in compounded interest doubles itself in four years. In how many years it becomes 32 times of itself as the same rate of compound interest?

The simple interest on $600$ for 9 months is $27$. Find the interest rate.

Miss Liza lent $4,000$ in such a way that some amount was given to Mr. A at $3\%$ p.a. S.I. and rest amount to was given to B at $5\%$ p.a. S.I., the annual interest from both is $144$. Find the amount lent to Mr. A.

A certain sum of money was put at S.I. for $2.5$ years at a certain rate of S.I. p.a. Had it been put at $4\%$ higher rate, it would have fetched $500$ more. Find the sum of money.

Rs.$1,25,000$ is borrowed at compound interest at the rate of $2\%$ for the 1st year, $3\%$ for the second year and $4\%$ for the 3rd year. Find the amount to be paid after 3 years.

If Rs. 1,000\displaystyle Rs. \displaystyle \text{Rs. }1,000 be invested at interest rate of 5%\displaystyle 5\% and the interest be added to the principal every $10$ years, then the number in years in which it will amount to $Rs. \displaystyle \text{Rs. }2,000$ is:

Ready to Master Mathematics of Finance?

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

Start Practicing — It's Free