Question 1203137: I want to have 500,000 for retirement in 35 years. My account earns 4% interest, how much will I need to deposit in the account each month? How much interest will I earn?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Answers:
Deposit $547.21 per month.
Interest earned = $270,174.51
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Work Shown for part 1
The future value of annuity formula is
where- FV = future value of the account
- P = monthly payment or deposit
- i = monthly interest rate in decimal form
- n = number of months
Isolating for P gets us
Plug in these values- FV = 500,000
- i = 0.04/12 = 0.00333333333333 approximately
- n = 35*12 = 420 months
to get the following
 approximately
 rounding to the nearest penny
You need to deposit $547.21 per month, for 420 months (aka 35 years), to reach the retirement goal.
If you were to plug P = 547.20 into this formula
then the approximate result is FV = 499,993.57 which is a bit short of the goal
However, P = 547.21 will go a bit over the goal to reach FV = 500,002.71
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Work Shown for part 2
If interest wasn't accrued, then depositing $547.21 per month for 420 months yields 547.21*420 = 229,828.20 dollars.
Subtract this from the $500,002.71 mentioned earlier to determine the interest
interest = $500,002.71 - $229,828.20
interest = $270,174.51
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Further Reading
https://www.investopedia.com/retirement/calculating-present-and-future-value-of-annuities/
Handy calculators
https://www.calculatorsoup.com/calculators/financial/future-value-annuity-calculator.php
and
https://www.omnicalculator.com/finance/annuity-future-value
Answer by ikleyn(52756)  (Show Source):
You can put this solution on YOUR website! .
I am amazed at how inaccurately this task is presented.
It does not say that the account is a compound.
It does not say that the account is compounded every month.
Presented in this way, the problems is not ready to start solve it.
It is ready to start editing it and to start explain to visitor,
what the used terms mean and how the problem should be written.
For me, it is difficult to imagine that some professor or a teacher
could assign so inaccurately formulated task to his (or her) students.
It is not for the first time I see similar problem, presented so inaccurately:
I just saw this style a week or two ago.
Even for one minute, I can not imagine that this problem came " from a professor "
or from a textbook, because such " professors " and such textbooks do not exist.
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