Question

Ravi borrowed Rs 5000000 at 4% per annum for 2 years. Find the amount and interest
Ravi has to pay after 2 years if if compuded half yearly​

Answer 1

Given:-

• Principal = Rs.5000000
• Rate = 4%
• Time = 2 years

To find:-

• Amount and interest after 2 years of the interest is compounded half-yearly.

Solution:-

We know,

The formula to find the amount when the interest is compounded half-yearly is:-

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

Hence,

= $\sf{A = 5000000\bigg(1+\dfrac{4}{200}\bigg)^{2\times 2}}$

= $\sf{A = 5000000\bigg(1 + \dfrac{1}{50}\bigg)^4}$

= $\sf{A = 5000000\bigg(\dfrac{50+1}{50}\bigg)^4}$

= $\sf{A = 5000000\bigg(\dfrac{51}{50}\bigg)^4}$

= $\sf{A = 5000000\bigg(\dfrac{51}{50}\bigg)\bigg(\dfrac{51}{50}\bigg)\bigg(\dfrac{51}{50}\bigg)\bigg(\dfrac{51}{50}\bigg)}$

=> $\sf{A = 5412160.8}$

Therefore the amount will be Rs.5412160.8.

We know,

CI = Amount - Principal

=> CI = 5412160.8 - 5000000

=> CI = 412160.8

Therefore CI will be Rs.412160.8.

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Explore more:-

The formula to find amount when the interest is compounded annually:-

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

The formula to find amount when the interest is compounded quarterly:-

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

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