You are saving for retirement. To live comfortably, you decide that you will need $2.5 million dollars by the time you are 65. If today is your 30th birthday, and you decide, starting today, and on every birthday up to and including your 65th birthday, that you will deposit the same amount into your savings account. Assuming the interest rate is 5%, the amount that you must set aside each year on your birthday is closest to

The answer is $26086

Explanation:

Solution

Given that:

Future of Annuity = 2.5 million

The interest rate = 5%

Time period = 35 (65-30)

Now

The future of annuity = Annuity [ (1+rate) ^time period-1]/rate

Thus

$2,500,000 = Annuity[ (1.05) ^36-1]/0.05

$2,500,000 = Annuity[ (4.79186135) ]/0.05

$2,500,000 = Annuity (95.83632272)

$2,500,000=Annuity*95.83632272

Annuity=$2,500,000/95.83632272

=$26086

Therefore the amount hat you must set aside each year on your birthday is closest to $26086