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 10.4% 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.

Answer 1

Answer:

1.

PV = $19108.96057 rounded off to $19108.96

So, $19108.96057 have to be invested today at 10.4% p.a. rate for 40 years for it to turn into a million dollars.

2.

PV = $131634.7058 rounded off to $131634.71

So, $131634.7058 have to be invested today at 5.2% p.a. rate for 40 years for it to turn into a million dollars.

3.

Times more investment = 6.888637682 times rounded off to 6.89 times

Explanation:

1.

To calculate how much we need to invest today for it to turn into $1 million in 40 years at 10.4% per annum rate, we will use the Present value of a sum formula as we need to determine the present value of $1 million earned after 40 years from today. The formula for present value of a sum is,

PV = FV / (1+r)^t

Where,

• PV is present value
• FV is future value
• r is the rate of interest or return
• t is the time period in years

PV = 1,000,000 / (1+0.104)^40

PV = $19108.96057 rounded off to $19108.96

So, $19108.96057 have to be invested today at 10.4% p.a. rate for 40 years for it to turn into a million dollars.

2.

Half the percentage rate of 10.4% p.a. = 10.4% / 2  =  5.2%

PV = 1,000,000  /  (1+0.052)^40

PV = $131634.7058 rounded off to $131634.71

So, $131634.7058 have to be invested today at 5.2% p.a. rate for 40 years for it to turn into a million dollars.

3.

Times more investment = 131634.7058  /  19108.96057

Times more investment = 6.888637682 times rounded off to 6.89 times