Question

You are saving for retirement. To live​ comfortably, you decide you will need to save $ 4 million by the time you are 65. Today is your 33 rd ​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 9 %​, how much must you set aside each year to make sure that you will have $ 4 million in the account on your 65 th ​birthday?

Answer 1

Future Value of an Ordinary Annuity

Here, we have Future Value of the Ordinary annuity = $4,000,000

Annual interest rate (r) = 9.00% per year

Number of periods (n) = 33 Years [(65 Years – 33 Years + 1 Year), The 1 should be added, since the payments are made starting from today]

Annual payments (P) = ?

Therefore, Future Value of an Ordinary Annuity = P x [{(1+ r)ⁿ - 1} / r ]

$4,000,000 = P x [{(1 + 0.09)³³ - 1} / 0.09]

$4,000,000 = P x [(17.18202838 – 1) / 0.09]

$4,000,000 = P x [16.18202838 / 0.09]

$4,000,000 = P x 179.8003153

P = $4,000,000 / 179.8003153

P = $22,247

“Hence, the amount to be set aside each year will be $22,247”