Question

Vasudevan invested Rs. $60,000$ at an interest rate of $12\mathrm{\%}$ per annum compounded half-yearly, what amount would he get
(i)After $6$ months
(ii)After $1$ year

Answer 1

Hint: Here we will use the formula to find the amount A is $A=P{\left(1+{\displaystyle \frac{R}{100}}\right)}^n$ where A is the amount, P is principal, R is the rate of interest and n is the time period. Here we will take $n=1$ for the amount after six months and $n=2$ for the amount after one year, since the rate of interest is compounded half yearly.

Complete step-by-step answer:
Given that-
Principal, $P=\text{Rs }60,000$
Rate of interest, $R=12\mathrm{\%}$ per annum
$\Rightarrow R=6\mathrm{\%}per\text{6 months}$
(i)After $6$ months
Here, the interest is calculated half-yearly, $\therefore n=6\text{months = 1}$
Place values in the formula –
$A=P{\left(1+{\displaystyle \frac{R}{100}}\right)}^n$
$\therefore A=60000\times {\left(1+{\displaystyle \frac{6}{100}}\right)}^1$
Take LCM (Least common multiple) and simplify the above equation –
$$\begin{gathered} \Rightarrow A=60000\times {\left({\displaystyle \frac{100+6}{100}}\right)}^1 \\ \Rightarrow A=60000\times {\left({\displaystyle \frac{106}{100}}\right)}^1 \end{gathered}$$
Convert the above fraction in the decimal form-
$\Rightarrow A=60000\times (10.6)$
Simplify the above equation-
$\Rightarrow A=63600\text{ Rs}\text{.}$
(ii)After $1$ year
Here, the interest is calculated half-yearly, $\therefore n=12\text{months = 2}$
Place values in the formula –
$A=P{\left(1+{\displaystyle \frac{R}{100}}\right)}^n$
$\therefore A=60000\times {\left(1+{\displaystyle \frac{6}{100}}\right)}^2$
Take LCM (Least common multiple) and simplify the above equation –
$$\begin{gathered} \Rightarrow A=60000\times {\left({\displaystyle \frac{100+6}{100}}\right)}^2 \\ \Rightarrow A=60000\times {\left({\displaystyle \frac{106}{100}}\right)}^2 \end{gathered}$$
Convert the above fraction in the decimal form-
$\Rightarrow A=60000\times (10.6{)}^2$
Simplify the above equation-
$\Rightarrow A=67416\text{ Rs}\text{.}$
Hence, Vasudevan will get Rs. $63600$ and Rs. $67416$ respectively after six months and one year.

Note: Always convert the percentage rate of interest in the form of fraction or the decimals and then substitute further for the required solutions. Remember the difference between simple interest and compound interest and apply its concept wisely. Compound interest is the interest paid for the interest earned in the previous year. Be good in multiples and do simplification carefully. Do not forget to write the unit Rupees after calculation.