Question 1177628: If an individual determines that they would like to retire in 20 years with $500,000 as the future value that is in their IRA, which earns 6% compounded monthly, how much money (rounded to the nearest cent) should they be putting away into the account each month?
I need to see the calculations & answers please!
Homework question from Hans Beauvoir
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! To determine the monthly deposit needed to reach $500,000 in 20 years, we can utilize the future value of an ordinary annuity formula.
The future value of an ordinary annuity is given by:
```
FV = PMT * (((1 + r)^n - 1) / r)
```
Where:
* FV is the future value ($500,000)
* PMT is the monthly payment (what we want to find)
* r is the periodic interest rate (6% per year compounded monthly, so r = 0.06/12 = 0.005)
* n is the number of periods (20 years with monthly compounding, so n = 20 * 12 = 240)
Plugging in the values:
```
$500,000 = PMT * (((1 + 0.005)^240 - 1) / 0.005)
```
Solving for PMT:
```
PMT = $500,000 / (((1 + 0.005)^240 - 1) / 0.005)
```
```
PMT ≈ $1,285.17
```
Therefore, the individual should deposit approximately **$1,285.17** each month to reach their retirement goal.
Let me know if you would like to explore other scenarios, such as different interest rates or time horizons.
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