Mathematics for FinancePYQ Dec 21Question 1232 of 512
All Questions

A sum of money is put at 20%\displaystyle 20\% compound interest rate p.a. at which year the aggregated amount just exceeds the double of the original sum?

Options

A6
B5
C4
D3
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — 4

All Options:

  • A6
  • B5
  • C4
  • D3

Detailed Solution & Explanation

**Derivation of Time to Double Sum** Given: - Rate of Interest (r\displaystyle r) = 20%\displaystyle 20\% per annum compounded annually - We want to find the year n\displaystyle n where the accumulated amount just exceeds 2P\displaystyle 2P (double the principal). **Step 1: Set up the inequality** A>2PA > 2P P(1+r)n>2PP(1 + r)^n > 2P (1+0.20)n>2(1 + 0.20)^n > 2 (1.20)n>2(1.20)^n > 2 **Step 2: Evaluate for different values of n\displaystyle n** - For n=1\displaystyle n = 1: (1.20)1=1.20<2\displaystyle (1.20)^1 = 1.20 < 2 - For n=2\displaystyle n = 2: (1.20)2=1.44<2\displaystyle (1.20)^2 = 1.44 < 2 - For n=3\displaystyle n = 3: (1.20)3=1.728<2\displaystyle (1.20)^3 = 1.728 < 2 - For n=4\displaystyle n = 4: (1.20)4=2.0736>2\displaystyle (1.20)^4 = 2.0736 > 2 At n=4\displaystyle n = 4 years, the amount first exceeds double the principal. Hence, **Option C** is the correct answer.

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 for 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 for Finance?

Practice all 512 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free