Question

You are saving for retirement. To live​ comfortably, you decide you will need to save $3 million by the time you are 65 . Today is your 30 th ​birthday, and you​ decide, starting today and continuing on every birthday up to and including your 65 th ​birthday, that you will put the same amount into a savings account. If the interest rate is 8 % ​, how much must you set aside each year to make sure that you will have $ 3 million in the account on your 65 th ​birthday?

Answer 1

We need to calculate the yearly investment to be made in the savings account for 36 years (65-30+1)
We have been given the future value need after 36 years which is $ 3 million
Formula to calculate future value of annuity
FV = I*([(1+r)^n-1]/r)
where FV = future value of the investment
I = yearly investment
r = interest rate
n = number of years investment is made
Using the above formula we can calculate the value of I
Calculation of yearly investment
$3,000,000 = I*([(1.08^36)-1]/0.08)
$3,000,000 = I*187.10215
I = 3000000/187.10215
I = 16,034.02
The yearly investment should be $16,034.02