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A sum of money doubles itself in 5 years at simple interest. In how many years will it become 4 times itself?
10 years
12 years
15 years
20 years
15 years
If a sum becomes n times in t years at simple interest, the time taken to become m times is given by T2тАЛ=nтИТ1mтИТ1тАЛimesT1тАЛ.
Principal sum = P, Amount = 2P in time t1 = 5 years, Target Amount = 4P
Simple┬аInterest=100PimesRimesTтАЛ
If a sum becomes n times in t years at simple interest, the time taken to become m times is given by T2тАЛ=nтИТ1mтИТ1тАЛimesT1тАЛ.
Students often mistakenly assume compound interest rules and calculate using geometric progression (2Po4P in 10 years instead of 15 years).
Calculate Rate of Interest
When the sum doubles itself, the Simple Interest earned is equal to the principal P. Using the formula SI=100PimesRimesTтАЛ, we substitute SI=P and T=5.
P=100PimesRimes5тАЛ
Determine Rate (R)
Solving for R, we get the annual rate of interest.
R=5100тАЛ=20%┬аper┬аannum
Set Up Equation for 4 Times the Sum
To become 4 times itself, the total Interest must be 4PтИТP=3P. Let the required time be T2тАЛ.
3P=100Pimes20imesT2тАЛтАЛ
Calculate Required Time
Solving the equation for T2тАЛ, we find the total years needed.
T2тАЛ=20300тАЛ=15┬аyears
C is correct because the sum requires 15 years to become 4 times itself at the same simple interest rate.
Always distinguish between simple interest linear growth and compound interest exponential growth to avoid common traps in aptitude tests.
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