For the same principal amount, the compound interest for two years at $5\%$ per annum exceeds the simple interest for three years at $3\%$ per annum by Rs. $1125$ . Then the principal amount in rupees is

Entered answer:

✅ Correct Answer: 90000

We solve this using the relationship between compound interest and simple interest.

We need to find a principal amount where compound interest for 2 years at 5% per annum exceeds simple interest for 3 years at 3% per annum by Rs. 1125.

We let the principal amount = $P$

Simple Interest = Principal × Rate × Time ÷ 100

SI for 3 years at 3% = $P \times 3 \times 3 \div 100 = \tfrac{9P}{100}$

Compound Interest = $P[(1 + \tfrac{R}{100})^n - 1]$

CI for 2 years at 5% = $P[(1 + \tfrac{5}{100})^2 - 1]$

$= P[(1.05)^2 - 1] = P[1.1025 - 1] = \tfrac{10.25P}{100}$

Given: CI - SI = 1125

$\tfrac{10.25P}{100} - \tfrac{9P}{100} = 1125$

$\tfrac{1.25P}{100} = 1125$

$P = 1125 \times \tfrac{100}{1.25} = 90000$

Alternative approach using test value:

We test with P = Rs. 8000 (chosen to make calculations easy)

SI for 3 years at 3% = $8000 \times 3 \times 3 \div 100 = Rs. 720$

CI for 2 years at 5% = $8000 \times [(1.05)^2 - 1] = 8000 \times 0.1025 = Rs. 820$

Difference = 820 - 720 = Rs. 100

When difference is Rs. 100, principal is Rs. 8000

When difference is Rs. 1125, principal is: $8000 \times \tfrac{1125}{100} = Rs. 90000$

The test value method works because the difference between CI and SI is directly proportional to the principal amount. This means if we know the difference for any principal, we can find the required principal using simple proportion.

In competitive exams, choosing a convenient test value (like 8000) makes mental calculations faster than solving the complete algebraic equation.

Therefore, the principal amount is Rs. 90000

CAT 2024 Slot 2

Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is

CAT 2019 Slot 1

A person invested a total amount of Rs $15$ lakh. A part of it was invested in a fixed deposit earning $6\%$ annual interest, and the remaining amount was invested in two other deposits in the ratio $2: 1$ , earning annual interest at the rates of $4\%$ and $3\%$ , respectively. If the total annual interest income is Rs $76000$ then the amount (in Rs lakh) invested in the fixed deposit was

CAT 2019 Slot 2

Amal invests Rs $12000$ at 8% interest, compounded annually, and Rs $10000$ at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at $7.5 \%$ simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is

CAT 2022 Slot 1

Alex invested his savings in two parts. The simple interest earned on the first part at $15 \%$ per annum for $4$ years is the same as the simple interest earned on the second part at $12 \%$ per annum for $3$ years. Then, the percentage of his savings invested in the first part is

CAT 2023 Slot 1

Anil invests Rs. $22000$ for $6$ years in a certain scheme with $4 \%$ interest per annum, compounded half-yearly. Sunil invests in the same scheme for $5$ years, and then reinvests the entire amount received at the end of $5$ years for one year at $10 \%$ simple interest. If the amounts received by both at the end of $6$ years are same, then the initial investment made by Sunil, in rupees, is

CAT 2024 Slot 3

Aman invests Rs $4000$ in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after $3$ years to the value of the investment after $5$ years is $25: 36$ , then the minimum number of years required for the value of the investment to exceed Rs $20000$ is

For the same principal amount, the compound interest for two years at 5%5\%5% per annum exceeds the simple interest for three years at 3%3\%3% per annum by Rs. 112511251125. Then the principal amount in rupees is

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)

For the same principal amount, the compound interest for two years at $5\%$ per annum exceeds the simple interest for three years at $3\%$ per annum by Rs. $1125$ . Then the principal amount in rupees is