Simple Interest and Compound Interest Question 1 - CAT 2025

Find the Simple Interest per year:

Simple interest grows at a constant absolute rate over time.

○ Amount at 3 years = Rs. 13,920

○ Amount at 6.5 years = Rs. 18,960

The interest earned over the 3.5-year gap is:

Interest for 3.5 years = 18,960 − 13,920 = Rs. 5040

Interest per year = 5040 / 3.5 = Rs. 1440

• Find the Principal (P) and Rate (R):

Interest for 3 years = 1440 × 3 = Rs. 4320

P = 13,920 − 4320 = Rs. 9600

R = (1440 / 9600) × 100 = 15% per annum

• Calculate the Compound Interest:

The principal of Rs. 9600 is compounded half-yearly for 2 years at a 15% annual rate.

○ Half-yearly rate (R') = 15% / 2 = 7.5%

○ Total compounding periods (n) = 2 × 2 = 4 half-years

Amount (A) = 9600 × (1 + 7.5/100)⁴ = 9600 × (1.075)⁴

Computing the power expansion:

(1.075)² = 1.155625

(1.075)⁴ = (1.155625)² ≈ 1.335469

A ≈ 9600 × 1.335469 = Rs. 12,820.50

Total Interest Earned = 12,820.50 − 9600 = Rs. 3220.50 ≈ Rs. 3221

Correct Option: A

💡 FundaMakers Tip:

When computing compound interest with non-standard bases like (1.075)⁴, save time by using the Successive Percentage Rule (a + b + ab/100) or simple interest estimation. Two periods of 7.5% net a value of 7.5 + 7.5 + 0.5625 = 15.56%. Four periods will be slightly more than double that (15.56 + compounding effect ≈ 33.55%). Finding 33.55% of 9600 brings you directly to the correct option without running long decimal multiplications.