Question 1177628
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.