Question

What sum of money will amount to ₹ $ 15972 $ in three years at $ 10\% $ per annum compounded yearly?

Answer 1

Hint: Use the formula for compound interest. It is a simple formula based question. Since it is given interest is compounded annually we must use the formula for compound interest.

Complete step-by-step answer:
We know that, total amount in compound interest is given by
 $ A = P \times {\left( {1 + \dfrac{R}{{100}}} \right)^T} $
Where, $ A $ is amount
 $ P $ is principal amount
 $ R $ is the rate of interest per annum compounded yearly
 $ T $ is time period
Here we have
Amount, $ A = $ ₹ $ 15972 $
Rate per interest, $ R = 10\% $
Time, $ T = 3 $ years.
Now putting all the values in formula.
 $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $
We get,
 $ 15972 = P \times {\left( {1 + \dfrac{{10}}{{100}}} \right)^3} $
 $ \Rightarrow 15972 = P \times {\left( {1 + \dfrac{1}{{10}}} \right)^3} $
By cross multiplying, we get
 $ \Rightarrow 15972 = P \times {\left( {\dfrac{{10 + 1}}{{10}}} \right)^3} $
 $ \Rightarrow 157972 = P \times {\left( {\dfrac{{11}}{{10}}} \right)^3} $
 $ \Rightarrow 15972 = P \times \dfrac{{1331}}{{1000}} $
 $ \Rightarrow P = \dfrac{{15972 \times 1000}}{{1331}} $
 $ = \dfrac{{15972000}}{{1331}} $
 $ \Rightarrow P = $ ₹ $ 12000 $

Note: You should divide the numerator and denominator into the multiples of prime factors and then cancel out the common factors to simplify the fraction. It would be comparatively easy.