Question

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

Answer 1

Hint: Proceed the solution by using Simple interest and Compound interest formula.
According given data,
Principal (P) = Rs.32, 000
Rate (R) =$12\mathrm{\%}p.a$
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=$32,000\times {\displaystyle \frac{12}{100}}\times 3$
S.I=$11520$
Now let us find Compound interest (C.I) value, for finding C.I we have to find the Amount.
Amount=$P(1+R÷100{)}^n$ [Here n is the no. of year (Time (T))]
Amount=$32,000(1+12÷100{)}^3$
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.