Question

(3) Find the compound interest on 8000 at 15% for 1 year, if the interest is compounded semi-annually.​

Answer 1

Answer:

P=8000 r=15/2[interest for 6 months] n=2 half yearly

8000∗(1+15200)2−8000=C.I

8000∗1.075∗1,075−8000=9245−8000=Rs.1245

Answer 2

Answer:

${\sf {\pink{\underline{\underline {\red {GIVEN : }}}}}}$

P(principal) = ₹8,000.

R(rate %) = 15%.

T(time) = 1 year.

$\sf{\pink{\underline {\underline{\green{\sf{TO \: FIND : }}}}}}$

The compound interest if it is compounded semi - annually.

${\red{\underline{\underline {\sf {\red {SOLUTION : }}}}}}$

It is told here to find the interest which is to be Compounded semi-anually.

As we know that,

When a principal is compounded

semi - annually then we must divide the rate and time used to change i.e., The time must be multiplied by 2 and rate divided by 2.

Hence,

$\bf \green \implies {\underline{\boxed{\bf{\green{C. I. = Amount - Principal}}}}}$

$\sf \mapsto \: C. I. = p(1 + \frac{ \frac{r}{2} }{100} {)}^{{n} \times{2} } - 8,000$

$\sf \mapsto \: C. I. = 8,000(1 + \frac{15}{100 \times 2} {)}^{2} - 8,000$

$\sf \mapsto \: C. I. =( 8,\cancel{000} \times \frac{215}{10\cancel0} \times \frac{215}{1 \cancel{00}} ) - 8,000$

$\sf \mapsto \: C. I. = (\frac{8 \times 215 \times 215}{10} ) - 8,000$

$\sf \mapsto \: C. I. = ( \frac{3,69,80\cancel 0}{1\cancel 0} ) - 800 0$

$\sf \mapsto \: C. I. = 36,980 - 8,000 \:$

$\bold \gray \dag { \underline{ \boxed { \blue{ \bf \therefore \: C. I. = 28,980 \: ans.}}}}\bold \gray \dag$