Question

If amount on the principal of Rs. $6,000$ is written as $6000{[1+\frac{5}{100}]}^3$ and compound interest payable half yearly, then rate of interest p.a. is ____ and time in years is ______.

• A. $10\%$
• B. $1.5$

Answer 1

Compare the given amount with standard formula for time period and interest rate

Amount when interest is compounded can be calculated as

$A=P{(1+\frac{r}{100n})}^{nt}$ $...\left(i\right)$

where $A=$Amount

$P=$principal

$r=$rate of interest (in percent per annum)

$n=$ number of times interest is compounded in a year

$t=$time(in years)

Compare given equation for amount with standard result we get

$$\begin{gathered} P=6000 \\ \frac{r}{n}=5 \\ nt=3 \end{gathered}$$

As stated interest is compounded half yearly, which means interest is compounded twice in a year

Therefore $n=2$

$\Rightarrow$ $t=\frac{3}{2}=1.5$ years

$\Rightarrow$ $r=5\times 2=10\%$

Hence the time period is $1.5$ years and rate of interest is $10\%$ per annum.