Question

(3) Find compound interest on Rs 30000 for 2 years and 3 months at 40% per annum compounded annualy​

Answer 1

Given:-

• Principal = Rs.30000
• Time = 2 years 3 months
• Rate = 40%

To Find:-

• Compound Interest if the interest is compounded annually.

Solution:-

We are given the time as 2 years and 3 months. Let us convert this months into years.

3 months = $\sf{\dfrac{3}{12} = \dfrac{1}{4}}$

We know,

$\sf{A = P\bigg(1+\dfrac{r}{100}\bigg)^n}$

Now,

Let us calculate the Amount,

$\sf{A = 30000\bigg(1+\dfrac{40}{100}\bigg)^2\bigg(1+\dfrac{40}{400}\bigg)^{4\times \dfrac{1}{4}}}$

= $\sf{A = 30000\bigg(1+\dfrac{4}{10}\bigg)^2\bigg(1+\dfrac{1}{10}\bigg)^1}$

= $\sf{A = 30000\bigg(\dfrac{10+4}{10}\bigg)^2\bigg(\dfrac{10+1}{10}\bigg)^1}$

= $\sf{A = 30000\bigg(\dfrac{14}{10}\bigg)^2\bigg(\dfrac{11}{10}\bigg)^1}$

= $\sf{A = 30000\bigg(\dfrac{14}{10}\bigg)\bigg(\dfrac{14}{10}\bigg)\bigg(\dfrac{11}{10}\bigg)}$

= $\sf{A = 30\times 14\times 14\times 11}$

= $\sf{A = 64680}$

Now,

CI = Amount - Principal

Hence,

CI = 64680 - 30000

CI = 34680

Therefore the CI after 2 years 3 years if the interest is compounded annually will be Rs.34680.

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Explore More!!!

The formula used to calculate amount if the interest is compounded annually:-

• $\sf{A = P\bigg(2+\dfrac{r}{100}\bigg)^n}$

Formul used to calculate amount if the interest is compounded half-yearly.

• $\sf{A = P\bigg(1+\dfrac{r}{200}\bigg)^{2n}}$

Formula for calculating amount if the interest is compounded quarterly:-

• $\sf{A = P\bigg(1+\dfrac{r}{400}\bigg)^{4n}}$

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