Question

Find the compound interest when:
(a) principal = * 2000, rate = 5% p.a. compounded
annually and time
2 years.
​

Answer 1

Step-by-step explanation:

Given:-

• Principal (P) = Rs.2000

• Rate (r) = 5%

• Time (n) = 2 years

To Find:-

• The Compound Interest compounded annually.

Solution:-

To Find the Compound Interest , first we need to find the Amount.

As we know that the formula used for finding Amount is:-

$\boxed{ \sf \leadsto Amount = P \bigg(1 + \frac{r}{100} \bigg) ^{n} }$

Substituting the values:-

$\sf \implies A = 2000 \times \bigg(1 + \dfrac{5}{100} \bigg) ^{2}$

$\sf \implies A = 2000 \times \bigg( \dfrac{100 + 5}{100} \bigg) ^{2}$

$\sf \implies A = 2000 \times \bigg( \dfrac{105}{100} \bigg) ^{2}$

$\sf \implies A = 2000 \times \bigg( \dfrac{21}{20} \bigg) ^{2}$

$\sf \implies A = 2000 \times \dfrac{21 \times 21}{20 \times 20}$

$\sf \implies A = 2000 \times \dfrac{441}{400}$

$\sf \implies A = 5 \times 441$

$\sf \implies A = 2205$

$\therefore \underline{\: \: \underline{\: \sf Amount = Rs.2205 \:}\:\:}$

Compound Interest = Amount - Principal

= 2205 - 2000

= 205

$\underline{\boxed{\therefore \textsf{\textbf{ Compound \: Interest = Rs.205 }}}}$

Answer 2

☆Given Question:-

Find the compound interest when:

(a) principal = * 2000, rate = 5% p.a. compounded  annually and time  2 years.

☆Required Answer:-

The compound interest is Rupees 205.

☆Explaination:-

$\large\sf{Given:-}$

➭Principal:- Rupees 2000

➭Rate of interest:- 5% p.a.

➭Time:- 2 years

$\large\sf{To \:Find:-}$

➭Compound interest compounded annually

$\large\sf{Processing:- }$

➭For the first year, P:- Rupees. 2000, R:- 5%

$\sf{Formula \:Used:-}$

$\large{\boxed{\boxed{\tt{\pink{I=\frac{P \times R \times T}{100}}}}}}$

• By applying all values we get:-

$\implies{\tt{{I=\frac{2100\times 5\times 1}{100}}}}$

$\implies{\tt{105}}$

Amount for the first year is Rupees 105.

➭Amount for the second year:-

$\implies\tt{2100+ 105=2205}$

So, amount for the second year is Rupees 2205.

✦Final Amount= Rupees 2250

$\large\sf{Compound \:Interest:-}$

➭Formula:- Final Amount- Original Amount

$\implies \tt{2205-2000=205}$

So, the compound interest is Rupees 205.