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At what rate (in percentage) per annum simple interest will a sum of money double itself in 8 years?
5.6%
12.5%
5%
6.25%
12.5%
For a sum to become n times in T years, the rate is R=T(nтИТ1)├Ч100тАЛ. Here, n=2, so R=8100тАЛ=12.5%.
The principal sum doubles itself, meaning Amount A = 2P, in time T = 8 years, under simple interest.
R=T(nтИТ1)├Ч100тАЛ
For a sum to become n times in T years, the rate is R=T(nтИТ1)├Ч100тАЛ. Here, n=2, so R=8100тАЛ=12.5%.
Students often use the compound interest formula A=P(1+R/100)n instead of the simple interest formula, leading to incorrect results.
Define the relationship
Let the principal be P. If the amount doubles, then the final amount A is 2P. The simple interest SI earned is AтИТP=2PтИТP=P.
SI=P
Use Simple Interest formula
The formula for simple interest is SI=100P├ЧR├ЧTтАЛ. Substituting SI=P and T=8 years:
P=100P├ЧR├Ч8тАЛ
Solve for Rate R
Cancel P from both sides and solve for R:
1=1008RтАЛтЯ╣R=8100тАЛ=12.5%
B is correct because the rate calculation results in 12.5%, satisfying the condition of the sum doubling in 8 years.
This concept is frequently used in 'Time and Work' variations and banking aptitude questions regarding maturity periods of investments.
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