SOLUTION: 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 (ro

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.
RELATED QUESTIONS
If an individual determines that they would like to retire in 20 years with $500,000 as... (answered by Theo)

Willie owns and manages a number of real-estate rental properties in town and enjoys... (answered by solver91311)

1. Mike�s Sport Shop deposits $3,600 at the end of each year for 12 years at 7% annual... (answered by edward d,Hyot)

Suppose that you’d like to retire in 40 years and you want to have a future value of $... (answered by ikleyn)

1- Aya and Harumi would like to buy a house and their dream house costs $500,000. They... (answered by Theo)

Willie owns and manages a number of real-estate rental properties in town and enjoys... (answered by solver91311)

Craig and Susan Miller had just returned from their honeymoon trip in the Whitsundays.... (answered by Fombitz)

raig and Susan Miller had just returned from their honeymoon trip in the Whitsundays.... (answered by Alan3354)