Question

Find the amount of Rs. 36000 after 2 years, compounded annually. The rate of interest being 10% for the first year and 12% for the second year.

Answer 1

Hint: Here the principal amount is Rs.36000 and we are given that it is compounded annually with a rate of interest of 10% for first year and 12% for second year and using this the amount at the end of two years is given by the formula $A = P\left( {1 + \dfrac{{{R_1}}}{{100}}} \right)\left( {1 + \dfrac{{{R_2}}}{{100}}} \right)$.

Complete step by step solution:
We are given a principle amount
$ \Rightarrow P = 36000$
And we are given that it was compounded annually
And we are given two different rate of interests for each year
So now let the rate of interest for first year be ${R_1}$
$ \Rightarrow {R_1} = 10\% $
And the rate of interest for second year be ${R_2}$
$ \Rightarrow {R_2} = 12\% $
Therefore the amount at the end of 2 years will be
$ \Rightarrow A = P\left( {1 + \dfrac{{{R_1}}}{{100}}} \right)\left( {1 + \dfrac{{{R_2}}}{{100}}} \right)$
Now let's use the known values in this formula
\[
   \Rightarrow A = 36000\left( {1 + \dfrac{{10}}{{100}}} \right)\left( {1 + \dfrac{{12}}{{100}}} \right) \\
   \Rightarrow A = 36000\left( {1 + \dfrac{1}{{10}}} \right)\left( {1 + \dfrac{3}{{25}}} \right) \\
   \Rightarrow A = 36000\left( {\dfrac{{10 + 1}}{{10}}} \right)\left( {\dfrac{{25 + 3}}{{25}}} \right) \\
   \Rightarrow A = 36000\left( {\dfrac{{11}}{{10}}} \right)\left( {\dfrac{{28}}{{25}}} \right) \\
   \Rightarrow A = 36000\left( {\dfrac{{308}}{{250}}} \right) = 3600\left( {\dfrac{{308}}{{25}}} \right) \\
   \Rightarrow A = 144\times 308 = 44352 \\
 \]

Therefore the amount at the end of two years is Rs.44352.

Note :
Students may tend to use the formula of compound interest
$ \Rightarrow A = P{\left( {1 + \dfrac{R}{{100}}} \right)^t}$
But we don’t use this here because we are given different rates of interest for each year.
Compound interest makes your money grow faster because interest is calculated on the accumulated interest over time as well as on your original principal.
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from the simple interest where interest is not added to the principal while calculating the interest during the next period. Compound interest finds its usage in most of the transactions in the banking and finance sectors and also in other areas as well.