Respuesta :
Answer:
The annual rate of interest is 2.56%
Step-by-step explanation:
Given as :
Principal Amount investing every week = $25
Principal Amount investing in 5 years = $25 × 5 × 52 = p = $6500
The Amount adds after 5 years = A = $7380
Time period = t = 5 years
Let annual rate of interest = r %
Now, According to question
Amount after 5 years = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, $7380 = $6500 × [tex](1+\dfrac{\textrm r}{100})^{\textrm 5}[/tex]
Or, [tex]\dfrac{7380}{6500}[/tex] = [tex](1+\dfrac{\textrm r}{100})^{\textrm 5}[/tex]
Or, 1.135 = [tex](1+\dfrac{\textrm r}{100})^{\textrm 5}[/tex]
Or, [tex](1.135)^{\frac{1}{5}}[/tex] = 1 + [tex]\dfrac{r}{100}[/tex]
Or, 1.0256 = 1 + [tex]\dfrac{r}{100}[/tex]
Or, 1.0256 - 1 = [tex]\dfrac{r}{100}[/tex]
Or, 0.0256 = [tex]\dfrac{r}{100}[/tex]
∴ r = 0.0256 × 100
i.e r = 2.56
So, The rate of interest = r = 2.56
Hence, The annual rate of interest is 2.56% Answer
