Question

At what rate percent per annum simple interest will a sum of money double itself in 6 years?
$A$. 16.6
$B$. 14.6
$C$. 15.6
$D$. 13.6

Answer 1

Hint: Simple interest rate can be calculated by the relation $S.I=\dfrac{P\times R\times T}{100}$ where P is the principal or initial amount, R is the rate of interest in percentage, and T is the time period. Total amount after T years can be given by relation;Total Amount = Principal Amount + Simple Interest.Using these formulas find out the rate percent.

Complete step-by-step answer:
We know the relation of simple interest, time period and rate of interest is given as
$S.I=\dfrac{P\times R\times T}{100}...................\left( i \right)$
Where P is the principle amount i.e. the amount at which rate of interest will act for T years of time period. Now, we know that the total amount of the money after T years can be calculated by adding the initial or principal amount and simple interest on that amount with rate of interest for T years. Hence, we get
Total amount = Principal + Simple Interest……………….(ii)
Now, coming to the question, we need to calculate the rate of interest such that the total amount after 6 years will be double of the initial or principle amount. So, if the principal amount is P, then the total amount after 6 years will be 2P. Hence, simple interest from equation (ii) can be given as
2P = S.I + P
S.I = P……………….(iii)
Now, put the value of principal amount = P and S.I = P from equation (iii) and time period as 6 years. And suppose the rate of interest is R%. Hence, we get from equation (i) as
$\Rightarrow S.I=\dfrac{P\times R\times T}{100} \\\ \Rightarrow P=\dfrac{P\times R\times 6}{100} \\\ \Rightarrow R\times 6=100 \\\ \Rightarrow R=\dfrac{100}{6}=16.6$
Hence, option (a) is the correct answer.

Note: Don’t put S.I as two lines of the principal amount. Amount after the T period is given as two times of principle or initial amount. One may go wrong with the words, so be careful while putting values in the formula of $S.I=\dfrac{PRT}{100}$ .
Don’t use compound interest formula, students may get confused with both the formulae. We get a general result from the given problem that if the final amount becomes two times the principal amount then the rate of interest can be directly given as $\dfrac{100}{T}$ . Hence, we can use this result directly in future.