Question

Anita deposits Rs 1000 in a savings bank account. The bank pays interest at the rate of 5% per annum. What amount can Anita get after one year?

Answer 1

Hint: We use simple interest formula $A=P\left( 1+\dfrac{rn}{100} \right)$ where $P$ is the initial principal sum , rate of interest in percentage , $n$ is the time period in years and $A$ is the amount accumulated after time period $n$. We put the known values as given in the question and find the unknown $A$.

Complete step-by-step solution:
We have to use here simple interest formula. We know from the simple interest formula that if the initial principal sum is $P$, the rate of interest in percentage is $r$, the time period in years is $t$, then the amount accumulated after time period $n$ is $A$ is given by
\[A=P\left( 1+\dfrac{rt}{100} \right)\]
We are given in the question that the initial principal sum which is the same amount Anita deposited as $P=1000$, the rate of interest in percentage which the bank pays as $r=5$, the time period in years is $t=1$. We are asked to find the amount Anita will get after 1 year that is $A$. So we put the given the known formulas and get,
\[A=1000\left( 1+\dfrac{5\times 1}{100} \right)=1000\left( 1+\dfrac{5}{100} \right)=1000\left( 1+0.05 \right)=1000\times 1.05=1050\]
So the bank will Anita 1050 rupees after 1 year. \[\]
We can alternatively first find the simple interest $I=PTR$ where $P$ is the initial amount deposited, $T$ is the time period and $R$ is the rate of interest in decimals. We are given in the question that $P=1000$rupees, $T=1$year and $R=5 \%=\dfrac{5}{100}=0.05$. So the interest generated is
\[I=PTR=1000\times 1\times 0.05=50\]
Anita after 1 year will get the sum of the amount deposited initially $P$ and the interest $I$. So the amount she will get in rupees is
\[A=P+I=1000+50=1050\]

Note: We need to take care of the confusion between simple interest and compound interest where compound frequency $n$ is involved and the new principal after 1 year is the sum of old principal and interest. The formula of compound interest is $A=P{{\left( 1+\dfrac{r}{100n} \right)}^{nt}}$.