Question

How much will Rs. 50,000 amount to in 3 years, compounded yearly, if the rates for the successive years are 6%, 8% and 10% respectively?

Answer 1

Hint: Here the interest is compound. So for the first year, calculate the compound interest by taking 6% interest rate for the principal amount 50,000, let this resulting amount be x. Then for the second year x will be the principal amount and the interest is 8%, calculate the resulting amount for the second year and let this amount be ‘y’. For the third year, y will be the principal amount and interest rate is 10%. In this way find the amount at the end of 3rd year.
Formula used:
Compound interest A is calculated by $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $ , where P is the principal amount, T is the time period and R is the interest rate.

Complete step-by-step answer:
We are given to find how much will Rs. 50,000 amount to in 3 years, compounded yearly, if the rates for the successive years are 6%, 8% and 10% respectively.
For the first year Principal amount P is Rs.50,000, interest rate R is 6%
Compound interest at the end of 1st year is
$\Rightarrow A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} = 50000{\left( {1 + \dfrac{6}{{100}}} \right)^1} $
For the second year, the above resulting amount will be the principal amount and R is 8%.
Compound interest at the end of 2nd year is
$\Rightarrow A = 50000\left( {1 + \dfrac{6}{{100}}} \right){\left( {1 + \dfrac{8}{{100}}} \right)^1} $
For the third year, the above resulting amount will be the principal amount and R is 10%.
Compound interest at the end of 3rd year is
$\Rightarrow A = 50000\left( {1 + \dfrac{6}{{100}}} \right)\left( {1 + \dfrac{8}{{100}}} \right){\left( {1 + \dfrac{{10}}{{100}}} \right)^1} = 50000\left( {\dfrac{{106}}{{100}}} \right)\left( {\dfrac{{108}}{{100}}} \right)\left( {\dfrac{{110}}{{100}}} \right) = \dfrac{{5 \times 106 \times 108 \times 11}}{{10}} = Rs.62,964 $
Therefore, Rs.50,000 in 3 years, compounded yearly, if the rates for the successive years are 6%, 8% and 10% respectively will amount to Rs.62,964.
So, the correct answer is Rs.62,964”.

Note: The interest can be either simple or compound. In simple interest, the interest amount does not change till the end of the return period whereas in compound interest, the interest amount gradually changes as the interest is imposed on the principal amount plus the previous accumulated interest combined. Compound interest is much greater than Simple interest.