Question

How long will an amount of money take to double at a simple interest rate of $2$ percent per annum?

Answer 1

Hint: The problem can be solved easily with the concept of simple interest. Interest is the amount of money gained on the principal over a certain period of time. We must remember the formula for simple interest. We will first assume the principal to be a variable, x. Then, the amount will be double of the principal. Then, we will substitute the value of rate of interest in order to get to the required answer.

Complete step-by-step answer:
In the given problem, let us assume the principal amount to be x rupees.
Then, Amount collected will be double of the principal amount. So, the amount collected is $ = 2x$.
We know that the total amount collected is the sum of interest and principal amount. So, the interest earned on the principal amount is $x$.
We are given the rate of interest as $2$ percent per annum.
Let the time take for the initial amount to double at a rate of interest of $2$ percent per annum be T years.
Now, we know the formula for the calculation of simple interest as $Interest = \dfrac{{P \times R \times T}}{{100}}$.
So, substituting the values of the known quantities, we get,
$ \Rightarrow x = \dfrac{{x \times 2 \times T}}{{100}}$
Isolating the variable T in the equation, we get,
$ \Rightarrow T = \dfrac{{100 \times x}}{{2 \times x}}$
Cancelling the common factors in numerator and denominator, we get,
$ \Rightarrow T = 50$
Hence, it will take fifty years for an amount to double at a simple interest of $2$ percent per annum.
So, the correct answer is “50 years”.

Note: Simple interest is very easy to calculate when we are given the principal amount, the time duration for which the loan is taken and the rate of interest charged by the institution which in this case is the bank. We must take care of the calculations to be sure of the final answer.