Simple Interest and Compound Interest Question 2 - CAT 2024
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:
Step-by-Step Explanation
Let Sunil's initial investment be X.
The scheme offers a 4% annual interest rate compounded half-yearly.
• Compounding rate per half-year = 4% / 2 = 2% (multiplier = 1.02).
• Anil's Final Amount (after 6 years):
Six years contains 6 × 2 = 12 half-yearly periods.
Amount = 22000 × (1.02)¹²
• Sunil's Final Amount (after 6 years):
Sunil stays in the scheme for 5 years (5 × 2 = 10 half-yearly periods):
Amount after 5 years = X × (1.02)¹⁰
He then reinvests this entire accumulated maturity amount for 1 year at 10% simple interest:
Amount = [X × (1.02)¹⁰] × (1 + 0.10) = X × (1.02)¹⁰ × 1.1
• Equate the final amounts:
X × (1.02)¹⁰ × 1.1 = 22000 × (1.02)¹²
X × 1.1 = 22000 × (1.02)²
X = 22000 / 1.1 × (1.02)²
X = 20000 × 1.0404 = 20808
Sunil's initial investment was Rs. 20808.
Correct Option: D
💡 FundaMakers Tip:
Never calculate high exponents like (1.02)¹² or (1.02)¹⁰ explicitly mid-exam. Keep them in index form. When you equate both sides, the powers of 1.02 cancel out perfectly, leaving behind a manageable difference of (1.02)². Spotting these algebraic cancellations keeps your workspace clean and prevents decimal fatigue.