Answer:
The rate of interest for the investment is 4.7%
Step-by-step explanation:
Given as :
The interest amount for investment = I = $250
The investment amount = p = $3500
The time period for investment = 18 months = 1.5 years
Let The rate of interest applied = r%
Now, From Compound Interest
Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
∵ Interest = Amount - Principal
So, I = A - p
Or, A = I + p
Or, A = $250 + $3500
i.e A = $3750
∴ A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, $3750 = $3500 × [tex](1+\dfrac{\textrm r}{100})^{\textrm 1.5}[/tex]
Or, [tex]\dfrac{3750}{3500}[/tex] = [tex](1+\dfrac{\textrm r}{100})^{\textrm 1.5}[/tex]
Or, 1.071428 = [tex](1+\dfrac{\textrm r}{100})^{\textrm 1.5}
Or, [tex](1.071428)^{\frac{1}{1.5}}[/tex] = [tex](1 + \dfrac{r}{100})[/tex]
Or, 1.047069 = [tex](1 + \dfrac{r}{100})[/tex]
Or, 1.047069 - 1 = [tex]\dfrac{r}{100}[/tex]
Or, 0.047069 = [tex]\dfrac{r}{100}[/tex]
∴ r = 0.047069 × 100
i.e r = 4.7069
So, The rate of interest = r = 4.7%
Hence, The rate of interest for the investment is 4.7% Answer
