Question

Sam invested Rs 15000 at the rate of 10 percent per annum for one year. If the interest is compounded half yearly, then the amount received by Sam at the end of the year will be:
$\begin{align}
  & \text{a) Rs 16500} \\
 & \text{b) Rs 16,525}\text{.50} \\
 & \text{c) Rs 16,537}\text{.50} \\
 & \text{d) Rs 18,150} \\
\end{align}$

Answer 1

Hint: Now in the question we are given with principal amount and rate of interest, and time. Now also since the Interest is compounded half yearly then the interest is compounded twice per year. Now we know the formula for amount is $A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}$hence we can find the amount with the help of this formula:

Complete step by step answer:
Now Sam Invested Rs 15000
This is nothing but our principal amount.
Hence we have principal amount (P) = Rs 15000. …………………..(1)
Now he has invested at the rate of 10 percent per annum.
Hence the rate of interest (r) = 10 percent = 0.1 ………………………. (2)
Now also the amount is invested for 1 year.
Hence we have time (t) = 1 …………………… (3)
We are given that the interest is compounded half yearly
Hence we have in one year the interest is compounded twice
Hence the value of n = 2 ………………. (4)
Now the formula for compound interest is given by $A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}$
Now substituting the values from equation (1), equation (2), equation (3) and equation (4) we get
$\begin{align}
  & A=15000{{\left( 1+\dfrac{0.1}{2} \right)}^{2(1)}} \\
 & =15000\times {{(1+0.05)}^{2}} \\
\end{align}$
$\begin{align}
  & =15000\times {{\left( 1.05 \right)}^{2}} \\
 & =15000\times (1.1025) \\
 & =16537.5 \\
\end{align}$
Hence the amount received by Sam by the end of year is 16537.5 Rs
Option c is the correct option.
Note:
Now note that in the question we have to take compound interest and not simple interest. Hence we will use the formula $A=P{{\left( 1+\dfrac{r}{n} \right)}^{nt}}$ . Also note that while taking rate of interest divide it by 100 since it is percentage.