Question

Sheetal deposited $ 20000 $ in the bank, where the interest credit is half-yearly. If the rate of interest paid by the bank is $ 6\% $ per annum, what amount will she get after $ 1 $ year.

Answer 1

Hint: In this question the amount of 1st year will be the next year principal. Time is $ 1 $ year and the interest is half –yearly,we will take time $ \dfrac{1}{2} $ in each step. Then, we will calculate the amount.
By using the formula of S.I $ = \dfrac{{P \times R \times T}}{{100}} $
Amount $ S.I + P $
Here, $ P = $ Principal sum
 $ R = $ Rate of interest
 $ T = Time $

Complete step-by-step answer:
 $ {P_1} = $ ₹ $ 20,000 $
\[{R_1} = 6\% \]
 $ {T_1} = \dfrac{1}{2}year $
Then,
S.I at the end of 1st year S.I $ = \dfrac{{{P_1} \times {R_1} \times {T_1}}}{{100}} $

S.I at the end of 1st year $ = \dfrac{{20,000 \times 6 \times \dfrac{1}{2}}}{{100}} $

S.I at the end of 1st year $ = \dfrac{{20,000 \times 6 \times 1}}{{100 \times 2}} $

S.I at the end of 1st year $ = 200 \times 3 $
S.I at the end of 1st year $ = $ ₹ $ 600 $
Amount at the end of 1st year \[ = {\text{ }}S.I + P\]
Amount at the end of 1st year $ = 600 + 20000 $
Amount at the end of 1st year $ = $ ₹ $ 20600 $

Here \[{P_2} = \]₹ $ 20600,{R_2} = 6\% ,\,{I_2} = \dfrac{1}{2}years $

S.I at the end of 2nd year $ = \dfrac{{{P_2} \times {R_2} \times {T_2}}}{{100}} $

S.I at the end of 2nd year $ = \dfrac{{20600 \times 6 \times 1}}{{100 \times 2}} $

S.I at the end of 2nd year $ = 206 \times 3 $
S.I at the end of 2nd year $ = $ ₹ $ 618 $
Now, amount at the end of 2nd year $ = S.I + P $
Amount at the end of 2nd year $ = $ ₹ $ 618 + 20600 $
Amount at the end of 2nd year $ = 21218 $
Hence, the required answer is ₹ $ 21218 $

Note: We can do this question by formula method of amount in half yearly $ T = 2 \times 1year = 2year\,\,and\,R = \dfrac{{6\% }}{2} = 3\% $
Amount $ = 20,000{\left( {1 + \dfrac{3}{{100}}} \right)^2} $
Amount $ = 20,000{\left( {1 + \dfrac{{100 + 3}}{{100}}} \right)^2} $
Amount $ = 20,000{\left( {1 + \dfrac{3}{{100}}} \right)^2} $
Amount $ = 20,000 \times {\left( {\dfrac{{103}}{{100}}} \right)^2} $
Amount \[ = 20,000 \times \dfrac{{103}}{{100}} \times \dfrac{{103}}{{100}}\]
Amount $ = 2 \times 10609 $
 $ Amount = $ ₹ $ 21218 $
Students should carefully put the exact value of $ P,R\,\,and\,\,T $ in the formula, otherwise you will get the wrong answer. One should check time, some time it is given in months, sometime in days and. So,you should convert into years.