Question

Q26)Find the compound
interest on Rs60,000 at the rate
of 10% per annum for 1.5 years
when interest is compounded
semi-annually.​

Answer 1

Given :-

• Principal = ₹60,000
• Rate = 10%
• Time = 1.5 years
• Interest is compounded semi annually (meaning half yearly)

Aim :-

• To find the Compound interest on the principal

Formula to use :-

In order to find the Compound interest we first have to find the amount

$\sf{Amount} = \sf{Principal}\bigg(1 + \dfrac{\sf{rate}}{200} \bigg)^{2\times \sf{time}}$

• Compound interest = Amount - Principal

Answer :-

Let us substitute the values to find the amount

• Let amount be A

$\implies\sf{A} = 60000\bigg(1+\dfrac{10}{200} \bigg)^{2\times1.5}$

By taking the LCM,

$\implies\sf{A} = 60000\bigg(\dfrac{200+10}{20}\bigg)^{3}$

By adding,

$\implies\sf{A} = 60000\bigg(\dfrac{210}{200} \bigg)^{3}$

By reducing to the lowest terms,

$\implies \sf{A} = 60000\bigg(\dfrac{21}{20} \bigg)^{3}$

$\implies \sf{A} = 60000 \times \dfrac{21}{20} \times \dfrac{21}{20} \times \dfrac{21}{20}$

By cancelling, we get :-

$\implies \sf{A} = 69457.5$

Therefore,

• Amount = ₹69457.5

Now that we have the value of the Amount and the Principal,

Compound interest :-

$\implies 69457.5 - 60000$

$\implies 9457.5$

Some more formulas :-

• When interest is compounded Annually :-

$\implies \sf{Amount} = \sf{Principal}\bigg(1+\dfrac{\sf{rate}}{100} \bigg)^{\sf{time}}$

• When interest is compounded quarterly :-

$\implies \sf{Amount} = \sf{Principal}\bigg(1 + \dfrac{\sf{rate}}{400} \bigg)^{4\times\sf{time}}$

• Simple interest :-

$\implies \sf{Simple \: Interest} = \dfrac{\sf{Principal}\times \sf{Rate} \times \sf{Time}}{100}$