Question

Find the amount and compound interest for Rs.16000 for 2 year at 10% per annum compounded half-yearly.

Answer 1

Hint: Here we go through by putting the formula of amount as we read in chapter compound interest because we have to find the amount and for the compound interest we subtract principal amount from the amount we find at the end of two years compounded half-yearly.

Complete step-by-step answer:
Here in the question it is given that a principal amount is Rs.16000 i.e. the given principal Amount (P) =RS.16000
The given time period (T) =2 years.
And the given rate(R) =10% compounded half-yearly.
Here the interest is compounded half yearly so n=2
Let us apply the formula of amount i.e. $A = P{\left( {1 + \dfrac{R}{n}} \right)^{nt}}$
Where,
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount) =Rs16000
r = the annual interest rate=10%
n = the number of times that interest is compounded per unit =2
t = the time the money is invested or borrowed for=2
Now put these value in formula we get,
$
   \Rightarrow A = 16000{\left( {1 + \dfrac{{10\% }}{2}} \right)^{2 \times 2}} \\
   \Rightarrow A = 16000{\left( {1 + \dfrac{{10}}{{2 \times 100}}} \right)^4} \\
   \Rightarrow A = 16000{\left( {\dfrac{{21}}{{20}}} \right)^4} \\
   \Rightarrow A = \dfrac{{16000 \times 21 \times 21 \times 21 \times 21}}{{20 \times 20 \times 20 \times 20}} \\
   \Rightarrow A = \dfrac{{{\text{194481}}}}{{10}} \\
  \therefore A = 19448.1 \\
 $
Therefore, compound interest= amount – principal amount=19448.1-16000=3448.1
Hence Amount=Rs.19448.1 and compound interest=Rs.3448.1

Note: Whenever we face such a type of question the key concept for solving the question is just simply put the formula in which the given terms of question are used and find out the unknown term that question asked by the help of that formula. Here in this question the principal amount, time and rate are given and we have to find the amount so we apply the formula of amount.