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A sum of money doubles itself in 8 years at simple interest. In how many years will it become 4 times the original amount at the same rate of interest?
16 years
20 years
24 years
32 years
24 years
Use the formula: T2тАЛT1тАЛтАЛ=n2тАЛтИТ1n1тАЛтИТ1тАЛ. Here, T2тАЛ8тАЛ=4тИТ12тИТ1тАЛ, which leads to T2тАЛ=8├Ч3=24 years.
A sum of money doubles itself (Amount = 2P) in 8 years at simple interest.
SI=100P├ЧR├ЧTтАЛ
Use the formula: T2тАЛT1тАЛтАЛ=n2тАЛтИТ1n1тАЛтИТ1тАЛ. Here, T2тАЛ8тАЛ=4тИТ12тИТ1тАЛ, which leads to T2тАЛ=8├Ч3=24 years.
Students often calculate the time to earn 4 times the interest, forgetting that the principal is already part of the total amount (n-1 interest needed).
Calculate rate of interest
If the sum doubles, the Simple Interest (SI) is equal to the principal (P). Using SI=P and T=8 years:
P=100P├ЧR├Ч8тАЛтЯ╣R=8100тАЛ=12.5%
Find time for 4 times the amount
To make the amount 4 times the principal, the interest must be 3 times the principal (SI=3P).
3P=100P├Ч12.5├ЧTтАЛ
Solve for Time
Solving for T by canceling P from both sides:
T=12.5300тАЛ=24
C is correct because the interest required to make the sum 4 times is 3 times the principal, which takes 3 times the duration of doubling.
This concept of proportional growth is identical to how you calculate time for maturity in simple annuity problems.
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