# Find the compound interest on Rs.9000 in 2 years at rate of 10 p.c.p.astep by step explain pls​

Find the compound interest on Rs.9000 in 2 years at rate of 10 p.c.p.a
step by step explain pls​

1. ### Given :

• Principal = Rs. 9000
• Time = 2 years
• Rate = 10 %

### Tofind :

• Compound Interest

### Concept Used :

→ Formula to calculate amount :-

$$\dag \overline{\underline{\boxed{\sf\pmb{ \red{Amount = P\Bigg[1 + \dfrac{r}{100}\Bigg]^n}}}}}$$

where,

• P = Principal
• r = rate
• n = Time

→ Formula to calculate Compound Interest :-

$$\dag \: \: \overline{ \underline {\boxed{ \sf{ \pmb{\red{Compound \: \: Interest = Amount – Principal}}}}}}$$

### Solution :

Amount :-

$$\\ \longmapsto \quad \sf Amount = P\Bigg[1 + \dfrac{r}{100}\Bigg]^n$$

$$\\ \longmapsto \quad \sf Amount = 9000\Bigg[1 + \dfrac{10}{100}\Bigg]^2$$

$$\\ \longmapsto \quad \sf Amount = 9000\Bigg[1 + \dfrac{1 \not0}{10 \not0}\Bigg]^2$$

$$\\ \longmapsto \quad \sf Amount = 9000\Bigg[1 + \dfrac{1}{10}\Bigg]^2$$

$$\\ \longmapsto \quad \sf Amount = 9000\Bigg[ \dfrac{10 + 1}{10}\Bigg]^2$$

$$\\ \longmapsto \quad \sf Amount = 9000\Bigg[ \dfrac{11}{10}\Bigg]^2$$

$$\\ \longmapsto \quad \sf Amount = 9000 \times \dfrac{11}{10} \times \dfrac{11}{10}$$

$$\\ \longmapsto \quad \sf Amount = 90 \not0 \not0 \times \dfrac{11}{1 \not0} \times \dfrac{11}{1 \not0}$$

$$\\ \longmapsto \quad \sf Amount = 90 \times \dfrac{11}{1} \times \dfrac{11}{1}$$

$$\\ \longmapsto \quad \sf Amount = 90 \times 11 \times 11$$

$$\\ \longmapsto \quad \sf \green {Amount = \:Rs. \: 10,890}$$

Compound Interest :-

$$\\ \longmapsto \quad \sf {Compound \: \: Interest = Amount – Principal}$$

$$\\ \longmapsto \quad \sf {Compound \: \: Interest = 10,890 – 9000}$$

$$\\ \longmapsto \quad \sf \green {Compound \: \: Interest = 1890}$$

$$\\ \longmapsto \quad \overline{\underline{\boxed{ \tt{ \pmb{\red {Compound \: \: Interest = 1890}}}}}}$$

1,890

Step-by-step explanation:

A=P(1+R/100)^n

A=9000(1+10/100)^2

A=9000(1+1/10)^2

A=9000(10×1+1/10)^2

A=9000(11/10)^2

A=9000(11/10×11/10)

A=90×11×11

A=90×121

A=10,890

C.I=A-P

C.I=10890-9000=1890