Question

calculate amount and compound interest on rupees 8000 for 1 year at 8% per annum compounded half yearly​

Answer 1

Answer:

$\huge{ \underline{ \rm{ \pink{ \large{Given:}}}}}$

• Principal (p) = Rs.8000
• Time (t) = 1 year
• Time (t) = 2 half years
• Rate of interest (r) = 8% (per annual)
• Rate of interest = 8/2 = 4% (half yearly)

$\huge{ \underline{ \rm{ \large{ \red{Find:}}}}}$

• Calculate amount and compound interest?

$\huge{ \underline{ \rm{ \green{ \large{Solution:}}}}}$

Now let's find the amount:-

We know that ⤵

${ \boxed{ \sf{Amount (A) = p \: {[1 + \frac{r}{100}] }^{n} }}}$

$\to{8000 {(1 + \frac{4}{100}) }^{2} }$

${ \to{8000 \times {( \frac{26}{25} )}^{2} }}$

${ \to{8000 \times { \frac{676}{625} } }}$

${ \to{8652.8}}$

So, Amount = Rs. 8652.8

Now let's find the Compound interest:-

We know that ⤵

${ \boxed{ \sf{Amount = Principal + Interest}}}$

$\to{ \sf{8652.8 =8000 + Interest }}$

${ \to{ \sf{ Interest = 8652.8 - 8000}}}$

${ \to{ \sf{ Interest = 652.8}}}$

$\: \: \:$

Therefore,

• Amount = Rs.8652.8

• Compound Interest = Rs. 652.8

Answer 2

Given:

rupees 8000 for 1 year at 8% per annum compounded half-yearly​

To Find:

calculate the amount and compound interest

Solution:

First, we need the formula to calculate the amount that is being compounded at some interest over a time period which goes as,

                                       $A=P(1+\frac{r}{n} )^{nt}$

Where,

           A= amount at the end of year

           P= Principal amount

           r= Rate of interest

           n= No of times the amount is being compounded

           t= Time period

Now put all the given values in the formula as stated above

P=8000

r=0.08

n=2

t=1

Therefore,

$A=8000(1+\frac{0.08}{2})^2\\=8000*1.0816\\=8652.8$

So the amount after a year will be Rs8652.8 and the interest will be,

$I=A-P\\=8652.8-8000\\=652.8$

and the interest after a year is Rs652.8

Hence, the amount and interest on Rs8000 after a year at 8% compounded half-yearly will be Rs8652.8 and Rs652.8 respectively.