Question

Find the
the amount and compound
interest on rs 10000 at 6%
per annum for 1 year, interest
being Compounded half-yearly​

Answer 1

Step-by-step explanation:

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

• Principal = Rs. 1000

• Rate = 6%

• Time = 1 year.

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

• The amount

• And the compound interest compounded annually.

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

Principal = Rs.1000

Rate = 6% per annum

For half - yearly

Rate = 6/2 = 3%

Time = 1 year = 2 half years.

As we know that

The amount is given by the formula

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

Here:-

• P = principal = Rs.1000

• A = amount = ?

• r = rate = 3%

• n = time = 2

Substituting the values:-

${ \rm \implies A = 1000\bigg(1 + \dfrac{3}{100} \bigg) ^{2} }$

${ \rm \implies 1000\bigg( \dfrac{100 + 3}{100} \bigg) ^{2} }$

${ \rm \implies 1000\bigg( \dfrac{103}{100} \bigg) ^{2} }$

${ \rm \implies 1000 \times \dfrac{103 \times 103}{100 \times 100} }$

${ \rm \implies 1000 \times \dfrac{10609}{10000} }$

${ \rm \implies \dfrac{10609}{10} }$

${ \rm \implies {1060.9}}$

$\boxed{\rm \pink{Amount = Rs.1060.9}}$

As we know that

The formula for Compound Interest is

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

= 1060.9 - 1000

= 60.9

$\boxed{\rm \purple{Compound\: Interest = Rs.60.9}}$