Mathematics of FinancePYQ May 25Question 4014 of 507
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Find the future value of an investment of ₹ 7,000 compounded quarterly at 10% per annum for 3 years.[Given that (1.025)12=1.34489\displaystyle (1.025)^{12} = 1.34489]

Options

A₹ 9,414.20
B₹ 7,435.73
C₹ 7,941.42
D₹ 8,000.00
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Correct Answer

Option a₹ 9,414.20

All Options:

  • A₹ 9,414.20
  • B₹ 7,435.73
  • C₹ 7,941.42
  • D₹ 8,000.00

Detailed Solution & Explanation

The formula for the future value of a compound interest investment is:
FV=P(1+rm)m×tFV = P \left(1 + \frac{r}{m}\right)^{m \times t}
Where:
- P=7,000\displaystyle P = ₹ 7,000 (Principal investment)
- r=10%=0.10\displaystyle r = 10\% = 0.10 (Nominal annual rate of interest)
- m=4\displaystyle m = 4 (Frequency of compounding per year, which is quarterly)
- t=3 years\displaystyle t = 3 \text{ years} (Duration of investment)

The interest rate per quarter is:
i=rm=10%4=2.5%=0.025i = \frac{r}{m} = \frac{10\%}{4} = 2.5\% = 0.025
The total number of compounding periods is:
n=m×t=4×3=12n = m \times t = 4 \times 3 = 12
Now, substitute these values into the future value formula:
FV=7000×(1+0.025)12=7000×(1.025)12FV = 7000 \times (1 + 0.025)^{12} = 7000 \times (1.025)^{12}
We are given that (1.025)12=1.34489\displaystyle (1.025)^{12} = 1.34489. Using this value, we calculate:
FV=7000×1.34489=9414.23FV = 7000 \times 1.34489 = 9414.23
Therefore, the future value is approximately 9,414.20\displaystyle ₹ 9,414.20.
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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