Answer:
The interest needed to reach that value of $6000 is 2.75%
Step-by-step explanation:
Given as :
The principal that invested in mutual fund = p = $4000
The time period = t = 15 years
The Amount after 15 years = A = $6000
Let The interest needed to reach that value = r%
Now, According to question
From Compound Interest method
Amount = principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, $6000 = $4000 × [tex](1+\dfrac{\textrm r}{100})^{\textrm 15}[/tex]
or, [tex]\dfrac{6000}{4000}[/tex] = [tex](1+\dfrac{\textrm r}{100})^{\textrm 15}[/tex]
Or, [tex]\frac{3}{2}[/tex] = [tex](1+\dfrac{\textrm r}{100})^{\textrm 15}[/tex]
or, 1.5 = [tex](1+\dfrac{\textrm r}{100})^{\textrm 15}[/tex]
or, [tex]1.5^{\frac{1}{15}}[/tex] = [tex](1+\dfrac{\textrm r}{100})[/tex]
or, 1.0275 = [tex](1+\dfrac{\textrm r}{100})[/tex]
or, 1.0275 - 1 = [tex]\dfrac{r}{100}[/tex]
or, 0.0275 = [tex]\dfrac{r}{100}[/tex]
∴ r = 0.0275 × 100
I.e r = 2.75
So, The interest needed to reach that value = r = 2.75%
Hence,The interest needed to reach that value of $6000 is 2.75% Answer
