The difference between the simple interest and the compound interest on a sum of money for 3 years at 10% per annum is ₹ 558. Find the sum.

Given :

The difference between the Simple Interest and the Compound Interest on a sum of money for 3 years at 10% per annum$=$ Rs. 558.

To find :

We have to find the sum.

Solution :

Let the sum be P.

Compound interest $=P[(1+\frac{r}{100})^n - 1]$

                                   $=P[(1+\frac{10}{100})^3 - 1]$

                                   $=P[(1+\frac{1}{10})^3 - 1]$  

                                   $=P[(\frac{11}{10})^3 - 1]$

                                  $=P[\frac{1331}{1000} - 1]$

                                  $=P[\frac{1331 - 1000}{1000}]$

                                 $=P[\frac{331}{1000} ]$

Simple interest $= \frac{P \times n \times r}{100}$

                          $= \frac{P \times 3 \times 10}{100}$

                         $= \frac{3}{10}P$

$CI - SI = 558$

$\frac{331}{1000}P -  \frac{3}{10}P = 558$

$\frac{331}{1000}P -  \frac{3 \times 100}{10 \times 100}P = 558$

$\frac{331}{1000}P -  \frac{300}{1000}P = 558$

$ \frac{31}{1000}P=558$

$ P = \frac{558 \times 1000}{31}$

$P = 18 \times 1000 = 18000$

Therefore, the sum is ₹18000.

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Updated on: 10-Oct-2022

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