Question

Ram invested 2500 each in two investment schemes viz, Compound Interest Scheme interest being compounded annually and Simple interest Scheme. If the difference between the Cl and Sl is 100 after 2 years, what is the rate of interest per annum it it is same for both the schemes?​

Answer 1

Answer:

The rate of interest is 20%

Step-by-step explanation:

Given that CI - SI = 100

We know that CI = $P(1+\frac{R}{100})^n - P$ - $\frac{PRT}{100}$ = 100

=> $P[(1+\frac{R}{100})^n -1-\frac{RT}{100}]$ = 100

=>  $2500[(1+\frac{R}{100})^2 -1-\frac{R*2}{100}]$ = 100

=>  $25[1^2+(\frac{R}{100})^2 + 2*1*\frac{R}{100} -1-\frac{2R}{100}]$ = 100

=>  $1+(\frac{R}{100})^2 + \frac{2R}{100} -1-\frac{2R}{100}$ = $\frac{1}{25}$

=>  $(\frac{R}{100})^2$ = $\frac{1}{25}$

=>   $(\frac{R}{100})^2$ = $(\frac{1}{5})^2$

=>  $\frac{R}{100}$ = $\frac{1}{5}$

=> R = $\frac{100}{5}$

=> R = 20

Therefore, the rate of interest is 20%