Question

At what rate percent per annum a sum of Rs. 1,800 will become Rs. 2,700 in 10 years?
A. 5%
B. 6%
C. 10%
D. 8%

Answer 1

Hint: Here, we will find the rate of percentage using the formula for calculating the simple interest, given by, $I=\left( \dfrac{PRT}{100} \right)$ where I is the interest, P is the principal amount, R is the rate of interest and T is the time period.

Complete step-by-step solution -
It is given in the question that a sum of Rs. 1,800 will become Rs. 2,700 in a time period of 10 years. So we have to find the rate percentage increased in the principal amount of Rs. 1,800 annually. We have been given the principal amount value as Rs. 1,800 and the time period as 10 years. Also, the final amount is given as Rs. 2,700. This means that the mean interest increased in 10 years can be found out by subtracting the initial amount from the final amount.
Interest amount = final amount - initial amount
= Rs. 2700 – Rs. 1800
= Rs. 900
Thus, the interest amount (I) in 10 years is Rs. 900
Now to find the percentage of annual rate we will use the formula of simple interest. We know that simple interest is given by the formula, $I=\left( \dfrac{PRT}{100} \right)$ where I is the interest, P is the principal amount, R is the rate of interest and T is the time period. So from the question we get, P = 1800, T = 10 years and also we have found out the value of I = Rs. 900. Now we have to find the value of the rate.
From $I=\left( \dfrac{PRT}{100} \right)$, we can write $R=\left( \dfrac{I\times 100}{P\times T} \right)$.
On substituting the values of I = Rs. 900, P = 1800 and T = 10 in the formula of rate, we get,
$R=\dfrac{900\times 100}{1800\times 10}=5%$
Thus, we get the rate percentage per annum as 5%. So option (A) is the correct answer.

Note: Students can directly use the formula of rate, $R=\left( \dfrac{I\times 100}{P\times T} \right)$ to find the rate percentage in this question. An alternative method of solving this question is as follows. As we have already calculated the value of interest amount as Rs. 900 for 10 years, we can use the unitary method to get the interest per year as $\dfrac{900}{10}=Rs.90$. It means that every year the person gets an increment of Rs.90 as an interest for Rs.1800. So the interest rate can be calculated as $\dfrac{90}{1800}\times 100=\dfrac{90}{18}=5%$.