Question

Principal- Rs. 200, Rate- 3%, Time-3 years. Find the difference of

SICI​

Answer 1

Given:

Principal- Rs. 200, Rate- 3%, Time-3 years. Find the difference between S.I. and C.I.?​

To find:

The difference between S.I. and C.I.

Solution:

​Method 1:

Principal, P = Rs. 200

Rate of interest, R = 3%

Time, T or n = 3 years

Simple Interest:

S.I. = $\frac{P \times R\times T}{100} = \frac{200 \times 3\times 3}{100} = Rs. \:18$

Compound Interest:

C.I. = $P[(1 + \frac{R}{100} )^n - 1] = 200 [(1 + \frac{3}{100} )^3 - 1] = 200 [(\frac{103}{100})^3 - 1 ] = Rs. \:18.54$

Therefore,

The difference between the C.I. and S.I. = Rs. 18.54 - Rs. 18 = Rs. 0.54

​Method 2:

Principal, P = Rs. 200

Rate of interest, R = 3%

Time, T or n = 3 years

A direct formula to find the difference between C.I. and S.I. is:

$\boxed{\bold{Difference \:between \:C.I. \:\&\:S.I. for\:3 \:years = P \bigg(\frac{R}{100} \bigg)^2\bigg(\frac{300 + R}{ 100} \bigg)}}$

Therefore,

The difference between the C.I. and S.I. is,

= $200 \bigg(\frac{3}{100} \bigg)^2\bigg(\frac{300 + 3}{ 100} \bigg)$

= $200 \times \frac{9}{10000} \times \frac{303}{ 100}$

= Rs. 0.54

Thus, The difference between the C.I. and S.I. is → Rs. 0.54

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