Question

16. If the CI on a sum of money for 3 years at the rate of 2% per annum is 306.04, then what will be the SI?
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Please tell by another method or by complete explaination. ​

Answer 1

The S.I. will be Rs. 300.

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Let's understand a few concepts:

To calculate the simple interest we will use the following formula:

$\boxed{\bold{Simple\:Interest = \frac{Principal \times Time\times Rate }{100} }}$

To calculate the compound interest we will use the following formula:

$\boxed{\bold{Compound\:Interest = P\bigg[\bigg(1 + \frac{R}{100} \bigg)^n - 1\bigg]}}$

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Let's solve the given problem:

Let "P" represents the sum of money (i.e., Principal)

The no. of years (T or n) = 3 years

The rate of interest (R) = 2% p.a.

The compound interest on a sum of money for 3 years at the rate of 2% per annum = Rs. 306.04

By using the above formula of C.I., we can form the equation as,

$306.04 = P\bigg[\bigg(1 + \frac{2}{100} \bigg)^3 - 1\bigg]}}$

$\implies 306.04 = P\bigg[\bigg( \frac{102}{100} \bigg)^3 - 1\bigg]}}$

$\implies 306.04 = P\bigg[\bigg(1.02\bigg)^3 - 1\bigg]}}$

$\implies 306.04 = P\bigg[1.061208 - 1\bigg]}}$

$\implies 306.04 = P\bigg[0.061208 \bigg]}}$

$\implies P = \frac{306.04}{0.061208}$

$\implies P = Rs.\:5000$

By substituting P = Rs. 5000, R = 2% p.a. and T = 3 years in the above formula of simple interest, we get

The simple interest will be,

= $\frac{5000\: \times\: 2 \:\times\: 3}{100}$

= $50 \:\times \:2\:\times\:3$

= $\bold{Rs.\:300}$

Thus, the simple interest will be Rs. 300.

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Answer 2

Step-by-step explanation:

Let "P" represents the sum of money (i.e., Principal)

The no. of years (T or n) = 3 years

The rate of interest (R) = 2% p.a.

The compound interest on a sum of money for 3 years at the rate of 2% per annum = Rs. 306.04

By using the above formula of C.I., we can form the equation as,

306.04 = P\bigg[\bigg(1 + \frac{2}{100} \bigg)^3 - 1\bigg]}}

\implies 306.04 = P\bigg[\bigg( \frac{102}{100} \bigg)^3 - 1\bigg]}}

\implies 306.04 = P\bigg[\bigg(1.02\bigg)^3 - 1\bigg]}}

\implies 306.04 = P\bigg[1.061208 - 1\bigg]}}

\implies 306.04 = P\bigg[0.061208 \bigg]}}

\implies P = \frac{306.04}{0.061208}⟹P=

0.061208

306.04

\implies P = Rs.\:5000⟹P=Rs.5000

By substituting P = Rs. 5000, R = 2% p.a. and T = 3 years in the above formula of simple interest, we get

The simple interest will be,

= \frac{5000\: \times\: 2 \:\times\: 3}{100}

100

5000×2×3

= 50 \:\times \:2\:\times\:350×2×3

= \bold{Rs.\:300}Rs.300

Thus, the simple interest will be Rs. 300.

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