Answer:
If you earn an annual return of 11%, then you need to invest 9,129.89
If you earn an annual return of 5.5%, then you need to invest 89,875.08
Step-by-step explanation:
We will calculate the first years in order to try to find a pattern. Let x be the initial investment.
1st year. We have our original amount of money plus the 11% of the original amount.
x + 0.11x = 1.11x
2nd year. We have the amount of money we had the 1st year plus the 11% of that amount.
1.11*x + 1.11*x*(0.11) = 1.11x*(1+0.11) = 1.11*x*(1.11) = (1.11^2)*x
3d year.
(1.11^2)*x + ((1.11^2)*x)*.11 = (1.11^2)*x*(1+0.11) = (1.11^2)*x*(1.11) = (1.11^3)*x
We can already see a pattern and say that, at year n, we will have:
(1.11^n)x
If we want to have 1,000,000 at age 45, then we just have to write the equation:
(1.11^45)=1 000 000
Solving for x we get that: x = 9,129.89
In an analogous way, we can write an equation for the case when the annual return is 5.5, in the following way:
(1.055^45)=1 000 000
Solving for x we get that: x = 89,875.08