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The difference between the simple interest and the compound interest on a sum of money for 3 years at 12% per annum is ₹216. Find the sum.
Given :
The difference between the simple interest the compound interest on a sum of money for 3 years at 12% per annum $=$ Rs. 216.
To find :
We have to find the sum.
Solution :
Let the sum be P.
Compound interest $= P[(1+\frac{r}{100})^n - 1]$
$= P [(1+\frac{12}{100})^3 - 1]$
$= P [(1+\frac{3}{25})^3 - 1]$
$= P [(\frac{28}{25})^3 - 1]$
$= P [\frac{21952}{15625} - 1]$
$= P[\frac{21952-15625}{15625}]$
$= \frac{6327}{15625}P$
Simple interest $= \frac{Pnr}{100}$
$= \frac{P \times 3 \times 12}{100}$
$= \frac{36P}{100} = \frac{9}{25}P$
$CI - SI = 216$
$ \frac{6327}{15625}P - \frac{9}{25}P = 216$
$ \frac{6327}{15625}P - \frac{9 \times 625}{25 \times 625}P = 216$
$\frac{6327}{15625}P -\frac{5625}{15625}P=216 $
$ \frac{6327 - 5625}{15625}P=216$
$\frac{702}{15625}P = 216$
$ P = \frac{216 \times 15625}{702}$
$P = \frac{337500}{702} = 4807.69$
Therefore, the sum is ₹4807.69.