Question

what is the compound interest on rs. 5000 in 2 years at the rate of 20% per annum? (interest compounded half yearly)​

Answer 1

Answer:

successive discount of 20% rate

at half yearly rate = 10% time = 4 cycle

overall rate for 4cycle = 46.41%

so, 5000×46.41%= 2320.5/-(ans)

Answer 2

Step-by-step explanation:

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

• Principal = Rs. 5000

• Time = 2 years.

• Rate = 20% per annum

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

• The Compound Interest compounded half yearly.

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

To find the Compound Interest, first we need to find the Amount.

Principal = Rs. 5000

Rate = 20% for one year

Rate = 10% for half yearly

Time = 2 years = 4 half years

As we know that:-

The formula for finding Amount is

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

Here:-

• P = Principal = 5000

• r = Rate = 10%

• n = time = 4

Substituting the values:-

${ \rm \implies 5000 \bigg(1 + \dfrac{10}{100} \bigg ) ^{4} }$

${ \rm \implies 5000 \bigg( \dfrac{100+10}{100} \bigg ) ^{4} }$

${ \rm \implies 5000 \bigg( \dfrac{110}{100} \bigg ) ^{4} }$

${ \rm \implies 5000 \bigg( \dfrac{11}{10} \bigg ) ^{4} }$

${ \rm \implies 5000 \times \dfrac{(11) ^{4} }{(10) ^{4} } }$

${ \rm \implies 5000 \times \dfrac{14641 }{10000 } }$

${ \rm \implies 7320.5}$

$\implies\underline{\underline{ \: \: \: \rm Amount = Rs. 7320.5 \: \: \: }}$

Now:-

Formula for finding Compound Interest is

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

${ = \rm 7320.5 - 5000}$

${ = \rm 2320.5 }$

$\underline {\boxed{ \rm \purple{ \therefore Compond \: Interest = Rs.2320.5} }}$