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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 the original sum at the same rate of interest?
10 years
12 years
15 years
20 years
15 years
For simple interest, the time taken to become n times is proportional to nтИТ1. Thus, T2тАЛ=2тИТ14тИТ1тАЛ├Ч5=15 years.
Principal = P, Amount = 2P in Time T1тАЛ = 5 years, Target Amount = 4P at the same simple interest rate.
T2тАЛ=n1тАЛтИТ1n2тАЛтИТ1тАЛ├ЧT1тАЛ
For simple interest, the time taken to become n times is proportional to nтИТ1. Thus, T2тАЛ=2тИТ14тИТ1тАЛ├Ч5=15 years.
Students often make the mistake of multiplying 5 years directly by 2 to get 10 years, ignoring that simple interest depends on the net interest earned (nтИТ1).
Analyze initial condition
When a sum doubles itself (A=2P), the simple interest earned equals the principal amount (SI=P) over the given time period of 5 years.
SI=P┬аfor┬аT=5┬аyears
Determine required interest for target amount
To make the sum 4 times itself (A=4P), the total interest required must be 3P (4PтИТP).
SInewтАЛ=4PтИТP=3P
Apply the shortcut formula
Using the direct proportion formula for simple interest, where n1тАЛ=2 and n2тАЛ=4: T2тАЛ=2тИТ14тИТ1тАЛ├Ч5.
T2тАЛ=13тАЛ├Ч5=15┬аyears
C is correct because the sum takes 15 years to yield an interest triple the principal, making the total amount 4 times the original.
Similar proportional reasoning can be used in compound interest problems, though compound interest follows an exponential growth pattern rather than linear.
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