In how many years will a sum of money double itself at 12% per annum? (a) 6 years 9 months (b) 7 years 6 months (c) 8 years 3 months (d) 8 years 4 months
ANSWER
Verified
Hint: Use a simple interest formula to determine the time required to get the money doubled. Use the formula, $S.I=\dfrac{P\times R\times T}{100}$ to determine the time. Here, P is the principal amount, R is the rate per annum and T is the time.
Complete step-by-step answer:
Let us come to the question. We have been given that the sum of money is doubled in a certain interval of time. Now, we use simple interest to calculate the interest over a certain period of time that is to be repaid to the money lender along with the principal amount. ‘A sum of money doubles itself’ means the interest that is formed on the borrower is equal to the principal amount because the total amount after a certain time interval is the sum of principal amount and interest formed. Mathematically,$A=P+S.I$, where A is the total amount, P is the principal amount and S.I is the simple interest.
Let us denote the rate with ‘R’ and time with ‘T’. Therefore, $\begin{align} & S.I=A-P \\ & =2P-P \\ & =P \\ \end{align}$
Using the formula, $S.I=\dfrac{P\times R\times T}{100}$, we get,
$P=\dfrac{P\times R\times T}{100}$ Cancelling the common term, we get, $\begin{align} & 1=\dfrac{R\times T}{100} \\ & T=\dfrac{100}{R} \\ \end{align}$
Substituting the value of $R$, we get, $\begin{align} & T=\dfrac{100}{12} \\ & \therefore T=8\dfrac{1}{4}\text{ years} \\ \end{align}$
Converting the fractional year into months, we have, $\begin{align} & T=8\text{ years + }\dfrac{1}{4}\times 12\text{ months} \\ & \text{=}8\text{ years 3 months} \\ \end{align}$ Hence, option (c) is the correct answer.
Note: We have converted the fractional year into month by multiplying the fraction with 12 because 1 year has 12 months. Also, the options were given according to years and months so we had to convert our answer according to the options. Don’t get confused in using simple interest or compound interest, here, simple interest is used because the information provided is applicable for simple interest only. If we were to use compound interest then some additional information would have been provided to us in the question.