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Calculate the amount and compound interest of $Rs28000$ for 1.5 years if the rate is $10\% $ per annum and compounded annually. Also find the simplest interest for the same. Which one is greater, simple or compound interest and by how much?

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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Hint: Here we need to find the compound interest and amount here. We will first find the compound interest using the formula and then we will find the amount. Then we will find the simple interest for the given years and then, at last, we will compare the simplest and compound interest i.e. which one is greater.

Complete step by step solution:
It is given that:
Principal amount $\left( P \right) = Rs28000$
Time $\left( T \right) = 1.5{\text{years}}$
Rate of interest $ = 10\% $
Now, we will calculate the amount for the first 1 year.
We know the formula to calculate the amount is given by
$ \Rightarrow A = P{\left( {1 + \dfrac{r}{{100}}} \right)^n}$
Now, we will substitute the value of principal amount and rate of interest here.
$ \Rightarrow A = 28000{\left( {1 + \dfrac{{10}}{{100}}} \right)^1} = 28000 \times \dfrac{{110}}{{100}}$
On further simplification, we get
$ \Rightarrow A = Rs.30800$
Now, we will find the compound interest.
We know that the compound interest is equal to the difference between the amount and the principal.
Therefore,
$CI = 30800 - 28000 = 2800$
Now, $Rs.2800$ will become the principal amount at the end of 1 year.
So we will find the simple interest for next $\dfrac{1}{2}year$.
We know the formula of simple interest is
$SI = \dfrac{{P \times R \times T}}{{100}}$
Now, we will substitute the value of principal amount, time and rate of interest in the formula of simple interest here
$ \Rightarrow SI = \dfrac{{2800 \times 10 \times 0.5}}{{100}}$
On further simplification, we get
$ \Rightarrow SI = Rs.140$
Therefore, the required compound will be equal to the sum of compound interest for 1st year and the simple interest for the next half year.
Therefore, required compound interest \[\] …………… $\left( 1 \right)$
Now, we will calculate the simple interest for given 1.5 years.
We know the formula of simple interest is
$SI = \dfrac{{P \times R \times T}}{{100}}$
Now, we will substitute the value of principal amount, time and rate of interest in the formula of simple interest here
$ \Rightarrow SI = \dfrac{{28000 \times 10 \times 1.5}}{{100}}$
On further simplification, we get
$ \Rightarrow SI = Rs.4200$ ……….. $\left( 2 \right)$

We can see that the simple interest is greater than the compound interest by $4200 - 2940 = 1260$ i.e. by $Rs.1260$.

Note:
Here we have calculated the compound interest and the simple interest using their formulas. Simple interest and compound interest is used in the banking and financial sectors. Compound interest is defined as the interest on a deposit or loan which is calculated based on both the initial principal and the accumulated interest from the previous periods. The other name of compound interest is compounding interest.