Mathematics of FinancePYQ Sept 25Question 4113 of 507
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Mohan invests ₹ 25,000 every year starting from today for next 5 years Interest rate is 7% per annum compounded annually. The future value of the annuity is ₹__________. (Given (1+0.07)5=1.40255\displaystyle (1+0.07)^5 = 1.40255)

Options

A1,46,768
B1,43,768
C1,45,768
D1,44,768
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Correct Answer

Option noneCorrect Option

All Options:

  • A1,46,768
  • B1,43,768
  • C1,45,768
  • D1,44,768

Detailed Solution & Explanation

Mohan invests ₹ 25,000 every year starting from today for 5 years at an interest rate of 7% per annum. Since the payments start today, this is an **annuity due**.
The future value of an annuity due is given by: FVdue=A[(1+i)n1i](1+i)FV_{\text{due}} = A \cdot \left[ \frac{(1+i)^n - 1}{i} \right] \cdot (1+i) where: - A=25,000\displaystyle A = 25,000 (annual investment) - i=0.07\displaystyle i = 0.07 (interest rate) - n=5\displaystyle n = 5 (number of periods) - Given: (1+0.07)5=1.40255\displaystyle (1+0.07)^5 = 1.40255
Substitute the values: FVdue=25,000[1.4025510.07]1.07FV_{\text{due}} = 25,000 \cdot \left[ \frac{1.40255 - 1}{0.07} \right] \cdot 1.07 FVdue=25,000[0.402550.07]1.07FV_{\text{due}} = 25,000 \cdot \left[ \frac{0.40255}{0.07} \right] \cdot 1.07 FVdue=25,0005.7507141.07FV_{\text{due}} = 25,000 \cdot 5.750714 \cdot 1.07 FVdue1,43,767.861.071,53,831.61 rupeesFV_{\text{due}} \approx 1,43,767.86 \cdot 1.07 \approx 1,53,831.61\text{ rupees}
However, if we calculate the future value of an **ordinary annuity**: FVordinary=25,000[1.4025510.07]=25,0005.7507141,43,768 rupeesFV_{\text{ordinary}} = 25,000 \cdot \left[ \frac{1.40255 - 1}{0.07} \right] = 25,000 \cdot 5.750714 \approx 1,43,768\text{ rupees} This corresponds to Option b, but it ignores the "starting from today" condition. Since 1,53,831.61\displaystyle 1,53,831.61 is not present in the options, none of the options represents the correct mathematical value for the annuity due. Therefore, the correct choice is "none".
Hence, **Option none** 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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