Shortcut Trick
Growth factor for two years = 1,50,528 ÷ 1,20,000 = 1.2544
Annual growth factor = √1.2544 = 1.12
For three years, the sum ₹P grows by a factor of 1.123 = 1.404928
∴ P = 3,51,232 ÷ 1.404928 = 2,50,000
∴ The correct answer is ₹2,50,000.
Alternate Method
Given:
Case 1: Principal (P1) = ₹1,20,000, Amount (A1) = ₹1,50,528, Time (t1) = 2 years
Case 2: Principal (P2) = ₹P, Amount (A2) = ₹3,51,232, Time (t2) = 3 years
Formula Used:
Compound Interest Amount, A = P(1 + r/100)t
Calculations:
⇒ For the first investment: 1,50,528 = 1,20,000 × (1 + r/100)2
⇒ (1 + r/100)2 = 1,50,528 ÷ 1,20,000 = 1.2544
⇒ 1 + r/100 = √1.2544 = 1.12
⇒ For the second investment: 3,51,232 = P × (1.12)3
⇒ 3,51,232 = P × 1.404928
⇒ P = 3,51,232 ÷ 1.404928
⇒ P = 2,50,000
∴ The correct answer is ₹2,50,000.
Additional Information
Compound Interest Formula
The amount A after t years is given by A = P(1 + r/100)t, where P is the principal and r is the annual interest rate.
Growth Multiplier
The term (1 + r/100) is the annual multiplying factor. If a sum grows for n years, the total multiplier is (1 + r/100)n.
Effective Rate of Interest
For a rate r compounded annually for 2 years, the effective interest rate is calculated as [r + r + (r × r)/100]%.