Question

You would like to be a millionaire when you retire in 40 years, and how much you must invest today to reach that goal clearly depends on what rate of return you can earn. First, suppose you can earn 10.7% per year, and calculate how much you would have to invest today. Second, suppose you can only earn half that percentage rate, and calculate how much you would have to invest today. Divide the second by the first, to see how many times more you must invest today at half that annual rate grow it to $1 million over 40 years. (Do not round the numbers in intermediate calculations, but enter your answer rounded to 2 decimal places (for example, 2.31).)

Answer 1

Answer:

I would need to invest 672,097.26 at 10.7% annual rate

If rate drops by half then the investment will be for  819,815.38

Explanation:

We are asked to to an invesmtent today to yield 1,000,000 in 40 years.

Notice this will be a lump sum not an annuity as this will be just one investment.

$Principal \: (1+ r)^{time} = Amount$

Amount 1,000,000.00

time 0.11

rate 40.00000

$Principal \: (1+ 40)^{0.107} = 1,000,000$

Principal at 10.7%   672,097.26

$Principal \: (1+ 40)^{0.0535} = 1,000,000$

Principal at 5.35%    819,815.38