Mathematics of FinanceMCQMTP May 19Question 1494 of 512
All Questions

200\displaystyle 200 invested at the end of each month in an account paying interest 6%\displaystyle 6\% per year compounded monthly. What is the future value of this annuity after 10\displaystyle 10th payment?

Options

A2045\displaystyle 2045
B2055\displaystyle 2055
C2044\displaystyle 2044
D2065\displaystyle 2065
For any discrepancies in this question, email contact@cadada.in

Correct Answer

Option a2045\displaystyle 2045

All Options:

  • A2045\displaystyle 2045
  • B2055\displaystyle 2055
  • C2044\displaystyle 2044
  • D2065\displaystyle 2065

Ad

Detailed Solution & Explanation

The future value (FV\displaystyle FV) of an ordinary annuity compounded monthly 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) = 6%\displaystyle 6\% p.a. * Periodic interest rate i=6%12=0.5%=0.005\displaystyle i = \frac{6\%}{12} = 0.5\% = 0.005 * Number of payments (n\displaystyle n) = 10\displaystyle 10 Substituting the values: FV=200[(1.005)1010.005]FV = 200 \left[ \frac{(1.005)^{10} - 1}{0.005} \right] Using (1.005)101.05114\displaystyle (1.005)^{10} \approx 1.05114: FV=200[1.0511410.005]=200×10.228=2,045.60FV = 200 \left[ \frac{1.05114 - 1}{0.005} \right] = 200 \times 10.228 = 2,045.60 Thus, the future value is approximately 2,045\displaystyle 2,045. 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

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

Related Comparison Tables

More Questions from Mathematics of Finance

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