Question

a money lenders lends a sum of rupees 2,000 at compound interest of 5%. the amount of received after 2 year each ​

Answer 1

Given

• Principal (P) = ₹ 2,000
• Rate (R) = 5%
• Time (N) = 2 years

Solution

$\fbox{\mathtt{ Amount = P ( 1 + \frac{R}{100} )^N }}$

$\mathtt{\implies\: 2,000 ( 1 + \frac{5}{100} )^2 }$

$\mathtt{\implies\: 2,000 × \frac{105}{100} × \frac{105}{100} }$

$\mathtt{\implies\: 2 × 105 × 10.5}$

$\mathtt{\red{\implies\: Rs\: 2,205}}$

$\fbox{\mathtt{Compound\: Interest = Amount - Principal}}$

$\mathtt{\implies\: C.I = Rs\: 2,205 - Rs\:2,000}$

$\mathtt{\green{\implies\: C.I = Rs\:205}}$

Answer 2

$\bf \large{ Given : }$

• Principal (P) = Rs 2000

• Rate (R) = 5%

• Time(T) = 2 years

$\bf \large{ To \: Find : }$

• Amount received after 2 years

$\bf \large{ Solution : }$

For the First Year :

$\bigstar \boxed{ \red{ \sf \: Simple \: Interest = \frac{P \times R \times T}{100} }}$

$\longrightarrow \sf \: \dfrac{20 \cancel0 \cancel0 \times 5 \times 1}{1 \cancel0 \cancel0}$

$\longrightarrow \sf \: Rs \: 100$

$\therefore$ Interest for the First Year = Rs 100

So,

$\bigstar \boxed{ \red{ \sf Amount = Simple \: Interest + Principal }}$

$\longrightarrow \sf \:100 + 2000$

$\longrightarrow \sf \:Rs \: 2100$

For the Second Year :

In Second Year, The Amount In the First Year becomes the Principal here.

$\bigstar \boxed{ \red{ \sf \: Simple \: Interest = \frac{P \times R \times T}{100} }}$

$\longrightarrow \sf \: \dfrac{21 \cancel0 \cancel0 \times 5 \times 1}{1 \cancel0 \cancel0}$

$\longrightarrow \sf \: Rs \: 105$

Amount at the end of 2 years :

$\bigstar \boxed{ \red{ \sf Amount = Simple \: Interest + Principal }}$

$\longrightarrow \sf \:105 + 2100$

$\longrightarrow \sf \:Rs \:2205$

Compound Interest for two years =

$\bigstar \boxed{ \red{ \sf Compound \: Interest = Amount \: - Principal }}$

$\longrightarrow \sf \: 2205 - 2000$

$\longrightarrow \sf \: Rs \:205$

Hence, Amount received by him after 2 years is Rs 2205 and Compound Interest is Rs 205