Question

Find the sum of money that amounts to $ Rs.31,740 $ in 2 years if the interest is compounded annually at the rate of 15% per annum.

Answer 1

Hint: The relation between principal amount, rate of interest and time period can be given by the formula, $ A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}} $ . So, using this formula, we will find the value of the principal amount invested for 2 years at a rate of interest of 15% per year so that the total amount will be $ Rs.31,740 $ .

Complete step-by-step answer:
In question we are given that a person invests some money for 2 years to earn compound interest at the rate of 15% per annum and he gets $ Rs.31,740 $ and we are asked to find the amount of money invested. So, first of all the given data can be given as,
 $ A=31740 $
 $ n=2 $
  $ R=15\% $
Where, A is the total amount invested, R is rate of interest and n is the time period for which the amount is invested.
Now, the formula for compound interest can be given as,
 $ A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}} $
Where, P is the principal amount invested. Here, A is $ Rs.31,740 $ , R is 15% per annum and n is 2 years, so on substituting these values in expression, we will get,
 $ A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}} $
 $ 31740=P{{\left( 1+\dfrac{15}{100} \right)}^{2}} $
on making P our subject and further simplifying the expression we will get,
 $ 31740=P{{\left( \dfrac{100}{100}+\dfrac{15}{100} \right)}^{2}} $
 $ 31740=P{{\left( \dfrac{115}{100} \right)}^{2}} $
 $ \Rightarrow \dfrac{31740\times 100\times 100}{115\times 115}=P $
 $ \Rightarrow P=\dfrac{31740\times 20\times 20}{23\times 23}=Rs.24000 $
Hence, the sum of money invested is $ Rs.24,000 $ .

Note: Sometimes students make mistake in selecting the formula between $ \dfrac{PRN}{100} $ and $ A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}} $ . If students use the formula $ \dfrac{PRN}{100} $ , then the answer will be $ 31740=\dfrac{P\times 15\times 2}{100} $ . On Solving we will get P as Rs. 105,800 which is completely wrong. Students should know that by using $ \dfrac{PRN}{100} $ , interest is directly calculated and by using $ A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}} $ directly amount is calculated. So, be careful while selecting the formula.