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A sum of money doubles itself in 8 years at simple interest. What is the rate of interest per annum?
10%
12.5%
15%
8%
12.5%
To find the rate when a sum becomes 'n' times in 'T' years, simply use R=T100тАЛ├Ч(nтИТ1). Here, doubling means n=2, so just calculate 100├╖8.
A sum of money doubles itself in Time (T) = 8 years at Simple Interest (SI).
R=T(nтИТ1)├Ч100тАЛ
To find the rate when a sum becomes 'n' times in 'T' years, simply use R=T100тАЛ├Ч(nтИТ1). Here, doubling means n=2, so just calculate 100├╖8.
Many students mistake 'doubling itself' as 200% interest, leading them to use n=200 instead of n=2 in the formula.
Define the variables
Let the principal be P. Since the amount doubles, the Final Amount A=2P. Therefore, Simple Interest SI=AтИТP=P.
SI=P
Apply the SI formula
Using the formula for Simple Interest SI=100P├ЧR├ЧTтАЛ, substitute the known values where SI=P and T=8.
P=100P├ЧR├Ч8тАЛ
Calculate Rate (R)
Cancel P from both sides of the equation and solve for R.
1=100R├Ч8тАЛтЯ╣R=8100тАЛ=12.5
B is correct because the calculated rate of interest is 12.5% per annum.
This formula is a specific case of the Simple Interest relationship. In Compound Interest problems, the calculation would involve powers (logarithms), so always confirm the interest type first.
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