Question

difference between simple interest and compound interest for 2 years is Rs.75 find the principal if the rate of interest is 15%​

Answer 1

Answer:
=C.I-S.I=75
=(P(100+R/100)^2-P)-(P*R*T/100)=75
=P(100+15/100)^2-1-(15*2/100)=75
=P(13,225/10000-1-30/100)=75
=P(225)=750000
=P=750000/225
=P=3333.33
The Principal is ₹3333.33(approx.)

Answer 2

Given:

Difference between simple interest and compound interest for 2 years is Rs.75

Solution:

Simple interest $\[ = \frac{{PRT}}{{100}}\]$

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

According to the question,

$\[ \Rightarrow P{\left( {1 + \frac{{15}}{{100}}} \right)^2} - P - \frac{{P \times 15 \times 2}}{{100}} = 75\]$

$\[ \Rightarrow P{\left( {1 + \frac{3}{{20}}} \right)^2} - P - \frac{{3P}}{{10}} = 75\]$

$\[ \Rightarrow P{\left( {\frac{{23}}{{20}}} \right)^2} - \frac{{13P}}{{10}} = 75\]$

$\[ \Rightarrow \frac{{529P}}{{400}} - \frac{{13P}}{{10}} = 75\]$

Take LCM,

$\[ \Rightarrow \frac{{529P - 520P}}{{400}} = 75\]$

$\[ \Rightarrow 9P = 30000\]$

$\[ \Rightarrow P = \frac{{30000}}{9}\]$

$\[ \Rightarrow P = 3333.33\]$

Hence, the principal is 3333.33 rupees.