In 35 years from today, you want to have enough money to do the following things
ID: 2661241 • Letter: I
Question
In 35 years from today, you want to have enough money to do the following things:
1. Withdraw $200,000 to live on for your first year of retirement
2. Each year after that, withdraw a payment that is 3% larger than the payment on your previous birthday, and
3. Give your favorite brother a gift of $50,000 in 45 years from today
Your account needs to have enough money for 20 years in retirement. Assume that you will continue to earn at 5% annual return during retirement.
1) In order to meet the retirement goal, what is the minimum amount of $$ you have to have in your account in 35 years, before you withdraw the $200,000?
2) Your plan is to begin making deposits into a new retirement account beginning on exactly 1 year from today, and make the same deposit each year unil the final deposit in 35 years. If your retirement acct pays 5% annual return, what is the minimum deposit you must make annually into the retirement acct to meet your goal?
Explanation / Answer
1)minimum amount of $$ you have to have in your account in 35 years = value of future withdrawals
= 200000+ 200000*1.03/1.05 + 200000*1.03^2/1.05^2+ .....200000*1.03^19/1.05^19 + 50000/1.05^10 = $3,291,476.77
2) Present value of deposits = present value of withdrawals
$3,291,476.77/1.05^35 = x/1.05 + x/1.05^2 + x/1.05^3.......x/1.05^34 + x/1.05^35
x= $36442.27
minimum deposit you must make annually into the retirement acct to meet your goal= $36442.27