The present value of your annuity is $83,000.00 and you want to make withdraws at the end of every 2 months for the next 6 years. If money is worth 5.5%, compounded every 2 months, what is the amount of your payments from the annuity for the next 6 years?

The payment would be $

To solve for the amount of the periodic payment from the annuity, we will use the formula for the present value of an ordinary annuity:

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

Where:
- $PV$ = Present Value of the annuity = $83,000.00
- $P$ = Amount of the periodic payment (what we need to find)
- $i$ = Interest rate per period
- $n$ = Total number of periods

### Step 1: Identify the known variables

- The interest rate is 5.5% per year, compounded every 2 months. To find the interest rate per period:
  \[
  i = \frac{5.5\%}{6} = 0.0091667
  \]
- The total number of periods is the number of two-month periods in 6 years. There are 6 periods per year, so:
  \[
  n = 6 \times 6 = 36 \text{ periods}
  \]

### Step 2: Solve for the payment $P$

We can rearrange the formula to solve for $P$:

\[
P = \frac{PV \times i}{1 - (1 + i)^{-n}}
\]

Substituting the known values:

\[
P = \frac{83,000 \times 0.0091667}{1 - (1 + 0.0091667)^{-36}}
\]

Let's calculate this.The amount of the periodic payment from the annuity for the next 6 years is approximately **$2,717.32** every 2 months.

Would you like any further details or clarification?

Here are 5 related questions:
1. How would the payment change if the interest rate were 6% instead of 5.5%?
2. What happens to the payment if withdrawals were made monthly instead of every 2 months?
3. How does changing the number of withdrawal periods (e.g., 5 years instead of 6) affect the payment?
4. Can you calculate the total amount of money withdrawn after 6 years?
5. How does the frequency of compounding affect the annuity's payment?

**Tip:** In an annuity, a higher interest rate or a longer term will generally result in smaller periodic payments.

The present value of your annuity is $83,000.00 and you want to make withdraws at the end of every 2 months for the next 6 years. If money is worth 5.5%, compounded every 2 months, what is the amount of your payments from the annuity for the next 6 years?

Learn how to calculate the periodic payment from an annuity with a present value of $83,000, compounded at 5.5% every 2 months over 6 years. This financial problem explores key concepts like present value, annuity payments, and compound interest, suitable for advanced high school or college-level students.

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