Find the present value PV of the annuity account necessary to fund the withdrawal given. (Assume end-of-period withdrawals and compounding at the same intervals as withdrawals. Round your answer to the nearest cent.)
$2,700 per month for 20 years, if the account earns 6% per year

To find the present value (PV) of an annuity, we use the formula for the present value of an ordinary annuity (since the withdrawals are made at the end of each period):

\[
PV = P \times \left(1 - \left(1 + \frac{r}{n}\right)^{-nt}\right) \div \left(\frac{r}{n}\right)
\]

Where:
- $ P $ is the payment per period ($2,700 per month),
- $ r $ is the annual interest rate (6% or 0.06),
- $ n $ is the number of compounding periods per year (since it's monthly withdrawals, $ n = 12 $),
- $ t $ is the time in years (20 years).

Now, let's calculate the PV.

\[
PV = 2700 \times \left(1 - \left(1 + \frac{0.06}{12}\right)^{-12 \times 20}\right) \div \left(\frac{0.06}{12}\right)
\]

I'll calculate this now.The present value (PV) of the annuity account necessary to fund the withdrawals is approximately **$376,868.08**.

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How does increasing the interest rate affect the present value of an annuity?
2. What happens to the PV if the payment period changes to quarterly instead of monthly?
3. How does reducing the withdrawal amount impact the PV?
4. Can the formula be used for withdrawals at the beginning of each period (an annuity due)?
5. How does the duration of withdrawals (e.g., 30 years instead of 20) affect the present value?

**Tip:** The longer the period of withdrawals, the higher the present value required for the annuity due to the extended time of payments.

Find the present value PV of the annuity account necessary to fund the withdrawal given. (Assume end-of-period withdrawals and compounding at the same intervals as withdrawals. Round your answer to the nearest cent.) $2,700 per month for 20 years, if the account earns 6% per year.

Calculate the present value of an annuity with monthly withdrawals of $2,700 over 20 years at 6% interest per year. This problem explains the time value of money and provides a detailed breakdown of the present value of an ordinary annuity formula.

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