Final answer:
To have $600,000 for retirement in 20 years with a 5% interest rate compounded monthly, you would need to deposit approximately $1,619.86 each month.
Step-by-step explanation:
To calculate the monthly deposit needed to have $600,000 for retirement in 20 years with a 5% interest rate compounded monthly, we can use the future value of an ordinary annuity formula. The formula is:
FV = P * [(1 + r)^n - 1] / r
Where FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of periods.
In this case, FV = $600,000, r = 5% / 12 = 0.004167, and n = 20 * 12 = 240. Plugging these values into the formula, we can solve for P:
$600,000 = P * [(1 + 0.004167)^240 - 1] / 0.004167
Simplifying the equation, we have:
600,000 = P * (1.004167^240 - 1) / 0.004167
Now, we can solve for P by isolating it on one side of the equation:
P = 600,000 * 0.004167 / (1.004167^240 - 1)
Using a calculator, we find that P is approximately $1,619.86. Therefore, you would need to deposit around $1,619.86 each month to have $600,000 for retirement in 20 years with a 5% interest rate compounded monthly.