Respuesta :
Answer:
The rate of interest is 9.5092%
Step-by-step explanation:
Given as :
The investment amount = p = $857
The Amount after 6 years = A = $1268.36
The time period = t = 6 years
Let The rate of interest = r%
Now, From Compound Interest method
Amount = Principle × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, $1268.36 = $857 × [tex](1+\dfrac{\textrm r}{100})^{\textrm 6}[/tex]
Or, [tex]\dfrac{1268.36}{857}[/tex] = [tex](1+\dfrac{\textrm r}{100})^{\textrm 6}[/tex]
Or, 1.48 = [tex](1+\dfrac{\textrm r}{100})^{\textrm 6}[/tex]
Taking power [tex]\dfrac{1}{6}[/tex] both side
So, [tex]1.48^{\frac{1}{6}}[/tex] = [tex]((1+\dfrac{r}{100})^{6})^{\frac{1}{6}}[/tex]
Or, 10.5092 = 1 + [tex]\dfrac{r}{100}[/tex]
Or, 10.5092 - 1 = [tex]\dfrac{r}{100}[/tex]
Or, 9.5092 = [tex]\dfrac{r}{100}[/tex]
∴ r % = 9.5092
So , The rate of interest = r = 9.5092 %
Hence, The rate of interest is 9.5092% Answer
