Question

Calculate the difference between the simple interest and the compound interest on RS 4000 in 2 years at 8% per annum compounded yearly

Answer 1

Step-by-step explanation:

Principal (P) = Rs.4000

Rate (R) = 8%

Time (T) = 2years

$\rm Simple \: Interest\: (SI) = \dfrac{PTR}{100}$

$\rm SI= \dfrac{4000 \times 2 \times 8}{100}$

$\rm SI= 40 × 16$

$\rm SI= 640$

$\rm \therefore Simple\: Interest= Rs.640$

Now, Compound Interest (CI) = Amount - Principal

$\rm Amount = P \bigg(1 + \dfrac{r}{100}\bigg)^{n}$

$\rm \dashrightarrow CI = \bigg[P \bigg(1 + \dfrac{r}{100}\bigg)^{n}\bigg] - P$

$\rm \dashrightarrow CI = \bigg[4000 \bigg(1 + \dfrac{8}{100}\bigg)^{2}\bigg] - 4000$

$\rm \dashrightarrow CI = \bigg[4000 \bigg(\dfrac{108}{100}\bigg)^{2}\bigg] - 4000$

$\rm \dashrightarrow CI = \bigg[4000 \times \bigg(\dfrac{27}{25}\bigg)^{2}\bigg] - 4000$

$\rm \dashrightarrow CI = \bigg[4000 \times \dfrac{27 \times 27}{25 \times 25}\bigg] - 4000$

$\rm \dashrightarrow CI =4665.6 - 4000$

$\rm \dashrightarrow CI =665.6$

$\rm \therefore Compound \: Interest= Rs.665.6$

The difference between Simple Interest and Compound Interest

= 665.6 - 640

= 25.6

The difference between Simple Interest and Compound Interest is Rs 25.60

Answer 2

Answer :-

25.6

Explanation :-

Given :

Principle,P => 4000

Time,n => 2 years

Rate,r => 8%

To Find :

Difference between the simple interest and the compound interest.

Solution :

Both simple interest and compound interest values are not given,so let’s find out their values first.

We know,

$\sf{}Simple\ interest=\dfrac{P\times r\times t}{100}$

$\sf{}:\implies \dfrac{4000\times 2\times 8}{100}$

$\sf{}:\implies \dfrac{64000}{100}$

$\sf{}:\implies \dfrac{640}{1}$

$\sf{}\therefore Rs.640$

Therefore,simple interest is equal to Rs.640

We know,

$\boxed{\sf{}C.I=Amount-Principle}$

We don’t know the amount here, so let’s find out the amount first.

For amount,

$\boxed{\sf{}A=P\bigg(1+\dfrac{r}{100}\bigg)^n}$

$\sf{}:\implies 4000\bigg(1+\dfrac{8}{100}\bigg)^2$

$\sf{}:\implies 4000\bigg(\dfrac{27}{25}\bigg)^2$

$\sf{}:\implies 4000\bigg(\dfrac{729}{625}\bigg)$

$\sf{}:\implies 4000\times \dfrac{729}{625}$

$\sf{}\therefore Rs.4665.6$

Therefore,

CI = 4665.6 - 4000

∴ 665.6

Therefore,compound interest  is equal to 665.6

Now, we know both simple interest and compound, so difference between the simple interest and the compound interest,

$\sf{}:\implies 665.6-640$

$\sf{}\therefore 25.6$

Hence,difference between the simple interest and the compound interest is equal to 25.6