Question

Find the amount and C.I. , if Rs. 9000 is invested for 24months at 12.5%p.a. interest is being compounded on yearly basis.​

Answer 1

Step-by-step explanation:

$\bf\underline{\underline{\red{Given:-}}}$

• Principal = Rs. 9000

• Rate = 12.5% p.a

• Time = 24 months

$\bf\underline{\underline{\blue{To\:Find:-}}}$

• The Amount

• Compound Interest compounded yearly.

$\bf\underline{\underline{\green{Solution:-}}}$

Time (n) = 24 months = 2 years

Principal (P) = Rs. 9000

Rate (R) = 12.5%

Now, the formula for calculating Amount is:-

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

$\rm = 9000 \times \bigg(1 + \dfrac{12.5}{100}\bigg)^{2}$

$\rm = 9000 \times \bigg(1 + \dfrac{1}{8}\bigg)^{2}$

$\rm = 9000 \times \bigg( \dfrac{8+1}{9}\bigg)^{2}$

$\rm = 9000 \times \bigg(\dfrac{9}{8}\bigg)^{2}$

$\rm = 9000 \times \dfrac{81}{64}$

$\rm = \dfrac{729000}{64}$

$\rm =11390.625$

$\underline{\boxed{\pink{\rm \therefore Amount = Rs. 11390.625}}}$

Now,

$\rm Compound\: Interest = Amount - Principal$

$\rm =11390.625 - 9000$

$\rm =2390.625$

$\underline{\boxed{\purple{\rm \therefore Compound\: Interest = Rs. 2390.625}}}$

Answer 2

Given :-

• Principal ( P ) = 9000

• Rate ( R ) = 12.5 %

• Time ( n ) = 24 months = 2 year

To Find :-

• Amount

• Compound interest

Solution :-

$\implies\underline{ \boxed{ \sf Amount=P \bigg(1 + \frac{r}{100} { \bigg)}^{n}}} \\ \\\implies \sf Amount=9000 \bigg(1 + \frac{12.5}{100} { \bigg)}^{2} \\ \\\implies \sf Amount = 9000 \bigg( 1 + \frac{1}{8} { \bigg)}^{n} \\ \\ \implies\sf Amount = 9000 \bigg( \frac{8 + 1}{8} { \bigg)}^{2} \\ \\ \implies \sf Amount = 9000 \bigg( \frac{9}{8} { \bigg)}^{2} \\ \\\implies \sf Amount = 9000 \times \frac{81}{64} \\ \\ \implies \sf Amount =11,390.625$

Now

$\implies \sf C.I= Amount - Principal \\ \\ \implies \sf C.I = 11390.625 - 9000 \\ \\ \implies \underline { \boxed {\sf C.I = 2390.625}}$