Question

Find the amount and the compound interest on 50000 for 1 years at 8% per annum,
the interest being compounded semi-annually.
​

Answer 1

Step-by-step explanation:

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

• Principal = Rs. 50000

• Time = 1 year.

• Rate of interest = 8%

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

• The amount

• The compound interest compounded semi - annually.

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

( Here:- semi - annually means half - yearly)

Rate = 8% per annum

For half year

Rate = 4%

Time = 1 year = 2 half years.

As we know that :-

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

Here:-

• n = time

• r = rate

• P = principal

Substituting the values:-

$\rm \implies Amount = 50000 \bigg(1 + \dfrac{4}{100} \bigg)^{2}$

$\rm \implies50000 \bigg( \dfrac{100 + 4}{100} \bigg)^{2}$

$\rm \implies50000 \bigg( \dfrac{104}{100} \bigg)^{2}$

$\rm \implies50000 \bigg( \dfrac{26}{25} \bigg)^{2}$

$\rm \implies50000 \times \dfrac{26 \times 26}{25 \times 25}$

$\rm \implies50000 \times \dfrac{676}{625}$

$\rm \implies54080$

$\boxed{ \rm\implies Amount = Rs. 54080}$

As we know that

Compound Interest = Amount - Principal.

= 54080 - 50000

= 4080

$\boxed{ \rm \therefore Compound \: Interest = Rs.4080}$