Simple Interest and Compound Interest Question 1 - CAT 2022
Why Simple Interest and Compound Interest is Important for CAT
Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is:
Step-by-Step Explanation
To avoid dealing with messy fractions, let us assume a smart value for the total initial capital based on the denominators 5 and 3.
- Let the total capital be 15 units.
Now, break down the investments:
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First Part: 1 / 5 × 15 = 3 units invested at 6% simple interest.
Annual Interest₁ = 3 × 0.06 = 0.18 units
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Second Part: 1 / 3 × 15 = 5 units invested at 10% simple interest.
Annual Interest₂ = 5 × 0.10 = 0.50 units
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Third Part: The remaining capital is 15 − (3 + 5) = 7 units invested at 1% simple interest.
Annual Interest₃ = 7 × 0.01 = 0.07 units
Sum the individual components to find the total annual interest income:
Total Annual Interest = 0.18 + 0.50 + 0.07 = 0.75 units
We want the cumulative interest over T years to equal or exceed the initial capital (15 units):
0.75 × T ≥ 15
T ≥ 15 / 0.75 ⇒ T ≥ 20 years
The minimum number of years required is 20.
💡 FundaMakers Tip:
Whenever a problem splits an unknown total value into fractional parts like 1 / 5 and 1 / 3, never start with X. Take the LCM of the denominators (5 × 3 = 15) and use it as your base number. This eliminates fractions instantly, turning potential calculation errors into clean mental math.