Question

Calculate the compound interest on ₹8000 at 9% per annum compounded half yearly

Answer 1

Answer: C.I = ₹736.2

Step-by-step explanation: Principal = ₹8000

                                             Rate = 9% per annum

                                                      = 9/2% per half yearly

                                             Time = 1 year

                                             Amount = P ( 1 + R/200)¹ ˣ ²

                                                           = 8000 ( 1 + 9/200)²

                                                           = 8000 × 209/200 × 209/200

                                                           = ₹8736.2

                                             C.I = ₹8736.2 - ₹8000

                                                  = ₹736.2

                                                     

Answer 2

Step-by-step explanation:

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

• Principal = Rs. 8000

• Time = 1 year

• Rate = 9% pet annum.

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

• The Compound Interest compounded half yearly.

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

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

$\rm Principal \: (P)= Rs. 8000$

$\rm Rate = 9\% \: per \:annum$

$\rm Rate\: for\: half\: year \: (r) = \dfrac{9}{2}\%$

$\rm Time \:(n) = 1 year = 2 half\: years$

Now, the formula for finding Amount is

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

$\rm = 8000 \times \bigg( 1+\dfrac{r}{100}\bigg)^{n}$

$\rm= 8000 \times \bigg( 1+\dfrac{ \frac{9}{2} }{100}\bigg)^{2}$

$\rm= 8000 \times \bigg( 1+\dfrac{ 9}{200}\bigg)^{2}$

$\rm= 8000 \times \bigg( \dfrac{ 200 + 9}{200}\bigg)^{2}$

$\rm= 8000 \times \bigg( \dfrac{ 209}{200}\bigg)^{2}$

$\rm= 8000 \times \dfrac{209 \times 209}{200 \times 200}$

$\rm= 8000 \times \dfrac{209 \times 209}{40000}$

$\rm= \dfrac{209 \times 209}{5}$

$\rm= \dfrac{43681}{5}$

$\rm= 8736.2$

$\implies\rm \underline{ \underline{ \: \: \: \: Amount= Rs. \:8736.2 \: \: \: \: }}$

Now:-

$\boxed{ \rm Compound \: Interest = Amount - Principal }$

$\rm= 8736.2 - 8000$

$\rm= 736.2$

$\underline{\boxed{\purple{\rm \therefore Compound \: Interest = Rs. 736.2}}}$