To find the periodic withdrawals (PMT) for an annuity account, we can use the formula for the present value of an annuity:

$PV = \dfrac{PMT \times \left(1 - (1 + r)^{-n}\right)}{r}$

Where:

• $PV$ is the present value (the initial amount in the account, $200,000).
• $PMT$ is the periodic withdrawal amount we need to find.
• $r$ is the interest rate per period (monthly in this case).
• $n$ is the total number of periods (months in this case).

Given Information:

• $PV = 200,000$
• Annual interest rate = 7%, so the monthly interest rate is $r = \dfrac{7\%}{12} = 0.005833$ (7% divided by 12 months).
• The time period is 19 years, so the total number of periods $n = 19 \times 12 = 228$ months.

Now, we rearrange the formula to solve for $PMT$:

$PMT = \dfrac{PV \times r}{1 - (1 + r)^{-n}}$

Substitute the values:

$PMT = \dfrac{200,000 \times 0.005833}{1 - (1 + 0.005833)^{-228}}$

Now, let's calculate this step by step.

$1 + r = 1 + 0.005833 = 1.005833$

$(1.005833)^{-228} \approx 0.25025$

$1 - 0.25025 = 0.74975$

$PMT = \dfrac{200,000 \times 0.005833}{0.74975} \approx \dfrac{1,166.6}{0.74975} \approx 1,556.29$

So, the periodic monthly withdrawal (PMT) is approximately $1,556.29.

Would you like a detailed breakdown of any step? Feel free to ask!

Here are some related questions:

1. What happens if the interest rate increases or decreases?
2. How do periodic withdrawals change if the number of years is shortened or extended?
3. How does the compounding frequency affect the periodic withdrawal amount?
4. What is the total amount withdrawn over the 19-year period?
5. What if the withdrawals were at the beginning of the period instead of the end?

Tip: If you're uncertain about the future, building a flexible annuity with varying withdrawal options can help adapt to changing needs.