Question

You have decided that you want to be a millionaire when you retire in 45 years. If you can earn an annual return of 11%, how much do you have to invest today? What if you can earn 5.5%? Submit your answers to this assignment.

Answer 1

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

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