Question

In how many years will a sum of money double itself at 4% per annum?
A) 8 years
B) 16 years
C) 12 years
D) 25 years

Answer 1

Hint: Use the given rate to calculate the simple interest with principal amount as the same as the interest received because the amount needs to get doubled according to the problem. Hence using this equation find the time in years required to double the amount.

Complete step-by-step answer:
Given the problem, we need to find the time in years in which a certain sum of money will double itself at an interest rate of 4%.
Let the sum or principal amount of money be Q.
Let the time for application of interest on the assumed principal amount be T.
The interest will be added on the principal amount in the form of simple interest with a rate of 4 % per annum as specified in the problem.
We know that simple interest is given by
$ \text{Simple Interest} = \dfrac {Q \times R \times T}{100} \to$ (1)
where Q denotes the principal amount, R denotes the rate of interest and T denotes the time period.
It is given in the problem that the annual interest rate ${\text{R}} = 4{\text{ }}\% $.
Also, it is given in the problem that the principal amount Q doubles itself after addition of interest.
This implies that the simple interest obtained on the principal amount after T years at a rate of 4 % is equal to the principal amount in the first place.
$ \Rightarrow {\text{Simple Interest}} = {\text{Q ----(2)}}$
Comparing the equations (1) and (2) and using ${\text{R}} = 4{\text{ % }}$, we get,
$
   \Rightarrow {\text{Simple Interest}} = {\text{Q}} = \dfrac{{{\text{Q}} \times 4 \times {\text{T}}}}{{100}} \\
   \Rightarrow {\text{Q}} = \dfrac{{{\text{Q}} \times 4 \times {\text{T}}}}{{100}} \\
   \Rightarrow \dfrac{{100}}{4} = {\text{T}} = 25{\text{ years}} \\
$
Hence the sum of money will double in 25 years.
Therefore, option (D). 25 years is the correct answer.

Note: Simple interest formula should be kept in mind while solving problems like above. It is important to note that the interest will not be double the principal amount as the interest gets added to the original amount to get the net sum of money. The rate should be used as the numerical value given in percent as the percent part is already defined in the formula used above. Simple interest is calculated on the principal, or original, amount. Compound interest is calculated on the principal amount and also on the accumulated interest of previous periods, and can thus be regarded as "interest on interest."