Simple Interest and Compound Interest Question 1 - CAT 2021
Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are ₹ 806.25 and ₹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to:
Step-by-Step Explanation
- Identify the properties of Compound Interest:
In a compound interest setup, the principal keeps growing geometrically year over year. A crucial consequence of this is that the individual interest amounts earned in consecutive years also grow by the exact same compounding factor (1 + r).
- Calculate the growth factor:
Let the interest in the second year be I₂ and the third year be I₃.
I₃ = I₂ × (1 + r)
866.72 = 806.25 × (1 + r)
1 + r = 866.72 / 806.25 = 1.075
(This implies the annual interest rate r is 7.5%)
- Calculate the fourth year's interest (I₄):
Using the same constant growth multiplier, the interest in the fourth year will be:
I₄ = I₃ × (1 + r)
I₄ = 866.72 × 1.075 = 931.724
Rounding to two decimal places, the interest accrued during the fourth year is ₹ 931.72.
Correct Option: C
💡 FundaMakers Tip:
Avoid the trap of creating full multi-variable formulas using Principal (P) and time periods (n). Remember this golden rule: Consecutive interest tranches in Compound Interest form a Geometric Progression (GP).
If you know I₂ and I₃, you can find I₄ directly through a simple ratio:
I₄ = (I₃)² / I₂ or I₄ = I₃ × (I₃ / I₂)
Recognizing this GP sequence saves you from long-form algebraic expansions.