Question

Find the difference between CI compounded annually and SI on 2000 for 3 years at the rate of 8 % per annum ​

Answer 1

Step-by-step explanation:

Principal (P) = Rs.2000

Time (T) = 3 years

Rate (R) = 8%

$\sf Simple \: Interest = \dfrac{ P \times T \times R}{100}$

$\sf \longrightarrow SI = \dfrac{ 2000 \times 3 \times 8}{100}$

$\sf \longrightarrow SI = \dfrac{ 2000 \times 3 \times 8}{100}$

$\sf \longrightarrow SI = \dfrac{48000}{100}$

$\sf\longrightarrow SI = 480$

$\sf \therefore \underline{Simple \: Interest = 480}$

Let, us find Compound Interest

Compound Interest = Amount - Principal

$\sf \longrightarrow CI = P \bigg(1 + \dfrac{r}{100} \bigg) ^{n} - P$

$\sf \longrightarrow CI = 2000\bigg(1 + \dfrac{8}{100} \bigg) ^{3} - 2000$

$\sf \longrightarrow CI = 2000\bigg[\bigg( \dfrac{100 + 8}{100} \bigg)^{3} - 1\bigg]$

$\sf \longrightarrow CI = 2000\bigg[\bigg( \dfrac{108}{100} \bigg)^{3} - 1\bigg]$

$\sf \longrightarrow CI = 2000\bigg[\bigg( \dfrac{27}{25} \bigg)^{3} - 1\bigg]$

$\sf \longrightarrow CI = 2000\bigg[ \dfrac{19683}{15625} - 1\bigg]$

$\sf \longrightarrow CI = 2000\times \dfrac{19683 - 15625}{15625}$

$\sf \longrightarrow CI = 2000\times \dfrac{27683 }{15625}$

$\sf \longrightarrow CI = \dfrac{8116000}{15625}$

$\sf \longrightarrow CI = 519.424$

$\sf \therefore \underline{Compound \: Interest = Rs.519.424}$

The difference between Compound Interest and Simple Interest

= CI - SI

= 519.424 - 480

= 39.424.

The difference between CI and SI = Rs.39.424