Question

Today, you turn 21. Your birthday wish is that you will be a millionaire by your 40th birthday. In an attempt to reach this goal, you decide to save $75 a day, every day, until you turn 40. You open an investment account and deposit your first $75 today. What rate of return must you earn to achieve your goal? Note: Ignore Leap Years.

Answer 1

Answer:

rate of 0.000171716533316905 = 0.017% daily

Explanation:

we need to solve for the rate of an annuity for 19 years with daily deposits of 75 dolllars to yield a principal of 1,000,000 dollars

365 days x 19 years = 6,935 days

we use goal seek on excel as follow:

on A1 we write 0.01 this will be a placeholder for the rate

then on A2 we write  =FV(A1;6935;75)

then with goal seek we definethat we want A2 equal to 1,000,000 changing A1 (rate)

which give us:

0.000171717  = 0.017% per day to achieve the goal:

$C \times \frac{(1+r)^{time} -1}{rate} = FV$  

C 75

time 6935

rate 0.000171717

$75 \times \frac{1-(1+0.000171716533316905)^{-6935} }{0.000171716533316905} = FV$  

FV $999,999.9999