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Let me re-formulate the post to make the problem formulation correct, precise and clear, as it should be.
You want to be able to withdraw $45,000 from your account at the beginning of each year for 25 years after you retire.
You expect to retire in 30 years.
If your account earns 9% interest compounded yearly, how much will you need to deposit at the end of each year
until retirement to achieve your retirement goals?
Solution
The solution is in 2 steps.
Step 1
Step 1 is to determine what amount you need to have at your account after 30 years depositing to it
in order for to be able to withdraw $45,000 from your account at the beginning of each year for 25 years after you retire.
The general formula to calculate this amount is
X = .
In this case the withdrawal semi-annual rate is W = $45000, the annual compounding rate
is r = 0.09, p = 1 + 0.09 = 1.09, the number of payment periods is n = 25. So
X = = 481,797.53 dollars.
Step 2
At this step we determine how big the annual deposit should be to provide this amount of $481,797.53 after 30 years of depositing.
This time it is classic Ordinary Annuity saving plan. The general formula is
FV = ,
where FV is the future value of the account; P is annual payment (deposit); r is the annual percentage yield presented as a decimal;
n is the number of deposits (= the number of years, in this case).
From this formula, you get for the annual payment
P = . (1)
Under the given conditions, FV = $481,797.53; r = 0.09; n = 30. So, according to the formula (1), you get for the annual payment
P = = $3534.64.
So, your annual deposit should be $3534.64. ANSWER
ANSWER. To provide your goal, you need to deposit $3534.64 dollars annually at the end of each year during 30 years.
Solved.
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If you want to learn the theory of this financing and/or see other similar solved problems, look into my lessons in this site
- Ordinary Annuity saving plans and geometric progressions
- Annuity Due saving plans and geometric progressions
- Solved problems on Ordinary Annuity saving plans
- Withdrawing a certain amount of money periodically from a compounded saving account
- Miscellaneous problems on retirement plans
Happy learning !