# Find the difference between CI and SI on Rs.32, 000 at $12\% p.a$ for $3$years.

Last updated date: 16th Mar 2023

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Answer

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Hint: Proceed the solution by using Simple interest and Compound interest formula.

According given data,

Principal (P) = Rs.32, 000

Rate (R) =$12\% p.a$

Time (T) = $3$years

Now let us get the simple interest value by using the formula of S.I

Simple interest (S.I) = $P \times T \times R$

On substituting P, T, R value in the above formula we get

S.I=$32,000 \times \dfrac{{12}}{{100}} \times 3$

S.I=$11520$

Now let us find Compound interest (C.I) value, for finding C.I we have to find the Amount.

Amount=$P{(1 + R \div 100)^n}$ [Here n is the no. of year (Time (T))]

Amount=$32,000{(1 + 12 \div 100)^3}$

Therefore Amount=$44928$

We know that Compound interest=Amount-Principal

So, Compound interest =$44928 - 32000$

Therefore Compound interest (C.I) =$12928$

Now, the difference between Compound interest and Simple interest is

Difference=$C.I - S.I$

Difference =$12928 - 11520$

Difference=$1408$

$\therefore $Difference between $C.I - S.I$=Rs.1408

NOTE: Here Simplification of formula is crucial. Here before finding the Compound interest we have found the amount which is not given in the problem.

According given data,

Principal (P) = Rs.32, 000

Rate (R) =$12\% p.a$

Time (T) = $3$years

Now let us get the simple interest value by using the formula of S.I

Simple interest (S.I) = $P \times T \times R$

On substituting P, T, R value in the above formula we get

S.I=$32,000 \times \dfrac{{12}}{{100}} \times 3$

S.I=$11520$

Now let us find Compound interest (C.I) value, for finding C.I we have to find the Amount.

Amount=$P{(1 + R \div 100)^n}$ [Here n is the no. of year (Time (T))]

Amount=$32,000{(1 + 12 \div 100)^3}$

Therefore Amount=$44928$

We know that Compound interest=Amount-Principal

So, Compound interest =$44928 - 32000$

Therefore Compound interest (C.I) =$12928$

Now, the difference between Compound interest and Simple interest is

Difference=$C.I - S.I$

Difference =$12928 - 11520$

Difference=$1408$

$\therefore $Difference between $C.I - S.I$=Rs.1408

NOTE: Here Simplification of formula is crucial. Here before finding the Compound interest we have found the amount which is not given in the problem.

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