Question

[5] Find the compound interest on Rs. 8000 at 15% for 1 year, if the interest is
compounded semi-annually,​

Answer 1

Answer:

4346.412192

Step-by-step explanation:

P=8000

i=0.075(15/100/2)

n=6(semi annually)

CI=P(1+i^n-1)

8000(1+0.75)^6-1)

8000(0.543301524)

=4346.412192

Answer 2

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

• P(principal) = ₹8,000.

• R(rate %) = 15%.

• T(time) = 1 year.

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

• The compound interest if it is compounded semi - annually.

${\pink{\underline{\underline {\sf {\purple {SOLUTION : }}}}}}$

• 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,

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

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

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

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

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

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

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

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

✪ Additional info :

• If time is given:- Half yearly, Quarterly , then rate and time is changed. So, for changing time , we have to multiply by 2 and for changing rate we have to divide by 2 if the time is given in half yearly, like this t×2 and r÷2. If time is given in quarter then we have to multiply by 4 in time and dividing by 4 in rate of interest.