Name: Difference Between Simple and Compound Interest
Uploaded: 2019-07-19
Duration: 3 min 57 s
Description: By now you have learned a lot about simple and compound interest. But do you know there is a big difference between the two? Find out what the differences are.

Question

Find the amount and the compound interest.

Principal $(₹)$	Rate (p.c.p.a.)	Duration (years)
$5000$	$8$	$3$

Accepted Answer

Compound interest is calculated based on the principal, interest rate and the time involved as follows:

If $P$ is the principal (the initial amount you borrow or deposit),

$r$ is the annual rate of interest,

$n$ is the number of years the amount is deposited or borrowed for

and, $A$ is the amount of money accumulated after n years, including interest,

then, the amount $8$ is given by, $A = p {(1 + \frac{r}{100})}^{n}$ .

Here, $p = ₹ 5000, r = 8 %$ and $n = 3$ years.

So, we get,

$A = ₹ 5000 \times {(1 + \frac{8}{100})}^{3}$

$\Rightarrow A = ₹ 5000 \times {(1 + \frac{2}{25})}^{3}$

$\Rightarrow A = ₹ 5000 \times {(\frac{27}{25})}^{3}$

$\Rightarrow A = ₹ 5000 \times \frac{27}{25} \times \frac{27}{25} \times \frac{27}{25}$

$\Rightarrow A = ₹ 6298.56$ .

Now, we have, the compound interest $=$ amount $-$ principal $= A - p = ₹ 6298.56 - ₹ 5000 = ₹ 1298.56$ .

Therefore, the required amount is $₹ 6298.56$ and the compound interest is $₹ 1298.56$ .

Principal $(₹)$	Rate $($ p.c.p.a. $)$	Duration $($ years $)$
$4000$	$7.5$	$2$

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