Mathematics of FinancePYQ May 25Question 4013 of 507
All Questions

The compound interest on a certain sum for 2 years at 10% per annum is ₹ 525. The simple interest on the same sum for double the time at half the rate percent per annum is -

Options

A₹ 400
B₹ 500
C₹ 600
D₹ 800
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — ₹ 500

All Options:

  • A₹ 400
  • B₹ 500
  • C₹ 600
  • D₹ 800

Detailed Solution & Explanation

Let the principal sum be P\displaystyle P.
The compound interest rate is R=10%\displaystyle R = 10\% per annum and the time period is T=2\displaystyle T = 2 years.
The compound interest (CI\displaystyle CI) formula is:
CI=P[(1+R100)T−1]CI = P \left[\left(1 + \frac{R}{100}\right)^T - 1\right]
Given that CI=₹525\displaystyle CI = ₹ 525:
525=P[(1+10100)2−1]525 = P \left[\left(1 + \frac{10}{100}\right)^2 - 1\right]
525=P[(1.1)2−1]525 = P \left[(1.1)^2 - 1\right]
525=P[1.21−1]525 = P \left[1.21 - 1\right]
525=0.21P525 = 0.21P
P=5250.21=2500P = \frac{525}{0.21} = 2500
So the principal sum is ₹2,500\displaystyle ₹ 2,500.

Now, we need to find the simple interest on this same sum (P=2500\displaystyle P = 2500):
1. For double the time: T′=2×2=4 years\displaystyle T' = 2 \times 2 = 4 \text{ years}
2. At half the rate percent: R′=10%2=5% per annum\displaystyle R' = \frac{10\%}{2} = 5\% \text{ per annum}

The simple interest (SI\displaystyle SI) formula is:
SI=P×R′×T′100SI = \frac{P \times R' \times T'}{100}
Substitute the values:
SI=2500×5×4100SI = \frac{2500 \times 5 \times 4}{100}
SI=25×20=500SI = 25 \times 20 = 500
Therefore, the simple interest is ₹500\displaystyle ₹ 500.
Hence, **Option B** 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

Compound Interest

Interest calculated on the initial principal, which also includes all of the accumulated interest of previous periods.

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\displaystyle 600 for 9 months is 27\displaystyle 27. Find the interest rate.

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

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

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

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

Ready to Master Mathematics of Finance?

Practice all 507 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free