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The image shows a financial problem involving present and future value calculations for annuities. Here is a breakdown of the problem based on what I can see:

- **You are going to receive $13,700 per year for five years. The appropriate interest rate is 8.6%.**
  
The following questions are asked:

1. **a.1:** What is the present value of the payments if they are in the form of an ordinary annuity? (No rounding of intermediate calculations, round final answer to 2 decimal places).
2. **a.2:** What is the present value if the payments are an annuity due? (Same rounding instructions).
3. **b.1:** What is the future value if the payments are an ordinary annuity? (Same rounding instructions).
4. **b.2:** What is the future value if the payments are an annuity due? (Same rounding instructions).

Here’s a general outline of how to approach these problems:

### Formulas:
1. **Present Value of an Ordinary Annuity (PVA):**
   \[
   PVA = P \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)
   \]
   where:
   - $ P $ = annual payment ($13,700),
   - $ r $ = interest rate per period (8.6% = 0.086),
   - $ n $ = number of periods (5 years).

2. **Present Value of an Annuity Due (PVAD):**
   The formula is the same as the ordinary annuity, but you multiply the result by $ (1 + r) $ to account for the earlier payments:
   \[
   PVAD = PVA \times (1 + r)
   \]

3. **Future Value of an Ordinary Annuity (FVA):**
   \[
   FVA = P \times \left(\frac{(1 + r)^n - 1}{r}\right)
   \]

4. **Future Value of an Annuity Due (FVAD):**
   Similar to the FVA but again multiplied by $ (1 + r) $:
   \[
   FVAD = FVA \times (1 + r)
   \]

### Let's calculate these values.

I will compute the results using these formulas and the given inputs.

Here are the results for the given financial calculations:

1. **Present Value of an Ordinary Annuity (a.1):** \$53,845.91
2. **Present Value of an Annuity Due (a.2):** \$58,476.66
3. **Future Value of an Ordinary Annuity (b.1):** \$81,339.57
4. **Future Value of an Annuity Due (b.2):** \$88,334.77

Would you like further details on any of these calculations, or do you have any other questions?

Here are five related questions:
1. What would happen to the present value if the interest rate were to decrease?
2. How does the timing of annuity payments (ordinary vs. annuity due) affect the future value?
3. Can these formulas be used for irregular payment intervals?
4. How does increasing the number of periods affect the future value of an annuity?
5. What is the impact of compounding frequency on these calculations?

**Tip:** An annuity due will always have a higher present and future value than an ordinary annuity due to the earlier timing of payments.

Suppose you are going to receive $13,700 per year for five years. The appropriate interest rate is 8.6%. What is the present value of the payments if they are in the form of an ordinary annuity and an annuity due? What is the future value of the payments as ordinary annuity and annuity due? (No rounding of intermediate calculations, round final answers to 2 decimal places)

Learn how to calculate the present and future values of annuities, including ordinary annuities and annuities due. Given $13,700 per year for five years at an interest rate of 8.6%, this example covers core financial concepts and time value of money calculations.

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