Question

You are saving for retirement. To live comfortably, you decide you will need to save $1 million by the time you are 65. Today is your 30th birthday, and you decide, starting today and continuing on every birthday up to and including your 65th 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 $1 million in the account on your 65th birthday? The amount to deposit each year is $ . (Round to the nearest dollar.)

Answer 1

FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / r)*(1+r)
Where:
P = the future value of an annuity stream	$       1,000,000
PMT = the dollar amount of each annuity payment	To be computed
r = the effective interest rate (also known as the discount rate)	8%
n = the number of periods in which payments will be made	36
So this will be annuity in advance for 35 annuities and the last amount will be paid on 65th birthday
1000000=	PMT x ((((1 + r) ^ n) - 1) / r)*(1+r) + PMT
1000000=	PMT * (((((1 + 8%) ^ 35) - 1) / 8%)*(1+8%))+1)
	PMT * 187.102
So the annual payment will be =	1000000/187.102
So the annual payment will be =	$         5,344.68