Shortcut Trick
In Simple Interest, the interest earned is directly proportional to the time period.
Interest required for an amount to double = P (1 time the principal)
Time taken to earn interest equal to the principal = 8 years.
New Principal = 25,000 and New Amount = 1,00,000 ⇒ Interest required = 75,000.
Since 75,000 is 3 times the principal (25,000), time required = 3 × 8 = 24 years.
∴ The correct answer is 24 years.
Alternate Method
Given:
An amount becomes double in 8 years.
New Principal (P2) = 25,000 and New Amount (A2) = 1,00,000.
Formula Used:
Simple Interest (SI) = (P × R × T) ÷ 100
Amount (A) = P + SI
P
2P
8 years
SI = P
25,000
1,00,000
T years
SI = 75,000 (3P)
Since SI is 3 times the Principal, Time = 3 × 8 = 24 years
Calculations:
Let the original principal be P.
⇒ Amount = 2P
⇒ SI1 = 2P − P = P
⇒ P = (P × R × 8) ÷ 100
⇒ R = 100 ÷ 8 = 12.5%
For the second case:
⇒ P2 = 25,000 and A2 = 1,00,000
⇒ SI2 = 1,00,000 − 25,000 = 75,000
⇒ 75,000 = (25,000 × 12.5 × T) ÷ 100
⇒ 75,000 = 250 × 12.5 × T
⇒ 75,000 = 3125 × T
⇒ T = 75,000 ÷ 3125 = 24 years
∴ The correct answer is 24 years.
Additional Information
Simple Interest Formula
SI = (P × R × T) ÷ 100, where P is the principal, R is the rate of interest, and T is the time period.
Amount Formula
Amount (A) = Principal (P) + Simple Interest (SI)
Shortcut for Multiples
If a sum becomes 'n' times in 'T' years at simple interest, then the Rate of Interest R = ((n − 1) × 100) ÷ T %.