LUMP SUM PROBLEM

Question

So you want to be a “millionaire” and you have 45 years to achieve it. What lump sum could you invest now to reach your goal, assuming that (on average) you receive an annual rate of return of 9% compounded monthly?

Answer 1

The Future Value of an investment is given by the formula FV = P(1+r)^t

where P = initial amount, r = annual rate, and t = time

 

in this case, the FV is $1,000,000, so we have to solve for P

 

First, we perform the calculation given by the value in the parenthesis, which is (1+0.09)⁴⁵, or ≅ 48.3

Our formula is now $1,000,000 = P48.3

 

rearranging the formula, we get $1,000,000/48.3 = P

 

so P ≅ $20,700