Question

Find the compound interest for the principal Rs.5000, r=4% p.a, n= 1 1/2 years, interest is compounded half yearly.

Answer 1

Given

• Principal= Rs 5000
• Rate = 4% Or 2% half yearly
• Time =1/2 years OR 2 half yearly

To Find

• Compound Interest

We know That

$~~~~~~~~~\boxed{\sf \pink{CI= P\{\left( 1+\dfrac{R}{100}\right) ^{n} -1\}}}$

Where

• P=5000
• R= 2%
• T= 2 years

On Subtuting The value in Formula

${\implies\sf {CI= 5000\{\left( 1+\dfrac{2}{100}\right) ^{2} -1\}}}$

${\implies\sf {CI= 5000\{\left( \dfrac{102}{100}\right) ^{2} -1\}}}$

$\implies\sf {CI= 5000\ \times ( (1.02) ^{2} -1)}$

$\implies\sf {CI= 5000\ \times ( 1.0404 -1)}$

$\implies\sf {CI= 5000\ \times 0.0404 }$

$~~~~~~~\underline{\boxed{\sf {CI= 5202}}}$

• The Compound Interest on Rs.5000, r=4% p.a, n= 1 1/2 years is Rs.5202

Answer 2

Answer:

Rs. 1340

Step-by-step explanation:

Concept= Compound Interest

Given= The principal, rate and time

To find= The Compound Interest half yearly

Explanation=

We have been asked to find the compound interest for the principal Rs.5000, r=4% p.a, n= 1 1/2 years, interest is compounded half yearly.

So Compound Interest is calculated as:

CI = A - P

Here A is the amount and P is the principal.

Amount = A = P( 1 + r/100)ⁿ

r = rate per annum and n= time in years

We have been told to find the Compound interest half yearly in such case the rate per annum is made half and the time is doubled.

Given:

Principal= P = Rs 5000

Rate = 4% p.a so half yearly will be 4/2 = 2%

Time = n = 11/2 years since it is half yearly so n*2 = 11/2 * 2 = 11

Therefore the compound interest will be calculated as :

CI= A - P

CI= P( 1 + r/100)ⁿ - P

CI = 5000( 1 + 2/100)¹¹ - 5000

=> 5000(102/100)¹¹ - 5000

=> 5000(1.02)¹¹ - 5000

=> 5000*1.268 - 5000

=> 6340 - 5000

=> 1340

CI= Rs 1340

Therefore the compound interest half yearly is Rs 1340.

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