Mathematics of FinancePYQ May 25Question 4321 of 507
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Dinesh received a cash bonus of ₹ 1,00,000 which he deposited in a bank which pays 10 percent interest compounded annually. How much approximate equal amount can Dinesh withdraw annually for a period of 10 years?[Given that (1.1)10=2.59374\displaystyle (1.1)^{10} = 2.59374]

Options

A₹ 16,273
B₹ 38,554
C₹ 62,745
D₹ 32,474
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Correct Answer

Option a₹ 16,273

All Options:

  • A₹ 16,273
  • B₹ 38,554
  • C₹ 62,745
  • D₹ 32,474

Detailed Solution & Explanation

This is a present value of an ordinary annuity problem where an initial deposit is made, and equal annual withdrawals are made from it.
Given details:
- Present Value (PV\displaystyle PV, initial bonus deposit) = 1,00,000\displaystyle ₹ 1,00,000
- Annual interest rate (i\displaystyle i) = 10%=0.10\displaystyle 10\% = 0.10
- Period (n\displaystyle n) = 10 years\displaystyle 10 \text{ years}
- A\displaystyle A = Equal annual withdrawal amount

The formula for the present value of an ordinary annuity is:
PV=A×[1(1+i)ni]PV = A \times \left[\frac{1 - (1 + i)^{-n}}{i}\right]
Substitute the values into the formula:
100000=A×[1(1.1)100.1]100000 = A \times \left[\frac{1 - (1.1)^{-10}}{0.1}\right]
We are given that (1.1)10=2.59374\displaystyle (1.1)^{10} = 2.59374. Therefore:
(1.1)10=12.593740.385543(1.1)^{-10} = \frac{1}{2.59374} \approx 0.385543
Substitute this back into the equation:
100000=A×[10.3855430.1]100000 = A \times \left[\frac{1 - 0.385543}{0.1}\right]100000=A×[0.6144570.1]100000 = A \times \left[\frac{0.614457}{0.1}\right]
100000=A×6.14457100000 = A \times 6.14457
Now solve for A\displaystyle A:
A=1000006.1445716274.54A = \frac{100000}{6.14457} \approx 16274.54
The equal annual withdrawal amount is approximately 16,273\displaystyle ₹ 16,273.
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.

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