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In what duration will a sum of money double itself at 20% per annum simple interest?
8 years
12 years
10 years
5 years
5 years
For a sum to double, Simple Interest must equal the Principal (SI = P). Using the formula SI = (P ├Ч R ├Ч T) / 100, we get P = (P ├Ч 20 ├Ч T) / 100, which simplifies to T = 100 / 20 = 5 years.
Rate of interest (R) = 20% per annum, Simple Interest (SI) is required such that the sum (P) doubles itself (Amount A = 2P).
T=P├ЧR(AтИТP)├Ч100тАЛ
For a sum to double, Simple Interest must equal the Principal (SI = P). Using the formula SI = (P ├Ч R ├Ч T) / 100, we get P = (P ├Ч 20 ├Ч T) / 100, which simplifies to T = 100 / 20 = 5 years.
Confusing 'double itself' with the total amount (A = 2P) and failing to subtract the original principal when calculating the interest, or using the compound interest formula by mistake.
Define the relationship
If the sum doubles, the Final Amount A must be twice the Principal P. Thus, A=2P.
A=2P
Calculate Simple Interest
The interest earned is the difference between the final amount and the principal. SI=AтИТP=2PтИТP=P.
SI=P
Apply the SI formula
Using the formula SI=100P├ЧR├ЧTтАЛ, substitute SI=P and R=20.
P=100P├Ч20├ЧTтАЛ
Solve for Time
Cancel P from both sides and solve for T: 1=10020├ЧTтАЛтЯ╣1=5TтАЛтЯ╣T=5.
T=5┬аyears
D is correct because 5 years is the required duration for the principal to earn interest equal to itself at a 20% annual rate.
This concept of 'doubling' is a classic test for simple vs compound interest; for compound interest, remember the Rule of 72, which approximates doubling time as 72/R.
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