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In what duration will a sum of money double itself at 5% per annum simple interest?
18 years
12 years
10 years
20 years
20 years
For doubling the money in simple interest, use the shortcut T=Rate100тАЛ. Here, T=5100тАЛ=20 years.
Sum of money (Principal) P = P, Total Amount A = 2P, Simple Interest Rate R = 5% per annum.
T=Principal├ЧRate100├Ч(AmountтИТPrincipal)тАЛ
For doubling the money in simple interest, use the shortcut T=Rate100тАЛ. Here, T=5100тАЛ=20 years.
Many students confuse Simple Interest with Compound Interest, where doubling would require the rule of 72 or logarithmic calculation.
Calculate Simple Interest
To double the money, the interest earned (SI) must be equal to the Principal (P), because Amount=P+SI=2P. Therefore, SI=P.
SI=P
Apply Simple Interest Formula
Use the SI formula SI=100P├ЧR├ЧTтАЛ where R=5% and SI=P.
P=100P├Ч5├ЧTтАЛ
Solve for Time (T)
Divide both sides by P and solve for T: 1=1005TтАЛ, which simplifies to T=5100тАЛ.
T=20┬аyears
D is correct because the time taken to double a sum at 5% simple interest is calculated as T=5100тАЛ=20 years.
In Compound Interest, the doubling time is approximately R72тАЛ using the Rule of 72, which is a common follow-up question type in competitive exams.
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