A financial company that advertises on television will pay you $46,000 now for annual payments of $8,000 that you are expected to receive for a legal settlement over the next 8 years. Use Exhibit 1-D.

What is the present value of the annual payments if you estimate the time value of money at 9 percent?

Note: Round your PVA factor to 3 decimal places and final answer to the nearest whole dollar.

Should you accept this offer?



To determine whether you should accept the company's offer, we need to calculate the **present value (PV)** of the annual payments using the **time value of money** formula. In this case, we need to calculate the **Present Value of an Annuity (PVA)** because the payments of $8,000 are received annually for 8 years.

### Step 1: Use the Present Value of an Annuity (PVA) formula

The Present Value of an Annuity formula is:

\[
PVA = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)
\]

Where:
- $ PVA $ = Present Value of the annuity (which we're calculating)
- $ PMT $ = Annual payment = $8,000
- $ r $ = Interest rate per period = 9% = 0.09
- $ n $ = Number of periods = 8 years

### Step 2: Find the Present Value Annuity Factor (PVA Factor)

The Present Value Annuity Factor (PVA Factor) can be calculated using the following formula:

\[
PVA \, Factor = \frac{1 - (1 + r)^{-n}}{r}
\]

Substitute the values $ r = 0.09 $ and $ n = 8 $:

\[
PVA \, Factor = \frac{1 - (1 + 0.09)^{-8}}{0.09}
\]

I'll calculate this.The Present Value Annuity Factor (PVA Factor) is approximately **5.535**.

### Step 3: Calculate the Present Value of the Annuity (PVA)

Now that we have the PVA factor, we can calculate the Present Value of the annuity by multiplying it by the annual payment ($ PMT $):

\[
PVA = PMT \times PVA \, Factor
\]

Substitute the values $ PMT = 8,000 $ and $ PVA \, Factor = 5.535 $:

\[
PVA = 8,000 \times 5.535
\]

Let me compute the final present value.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can manually calculate the present value of the annuity using the formula:

\[
PVA = 8,000 \times 5.535 = 44,280
\]

The present value of the payments is approximately **$44,280**.

### Step 4: Compare the Offer

The financial company is offering $46,000. Since $46,000 is **more** than the present value of $44,280, it may be worth considering the offer.

---

Do you want details or have any questions?

Here are some related questions:
1. How does increasing the interest rate affect the present value?
2. What if the payments lasted for 10 years instead of 8?
3. How would a 12% interest rate change the present value?
4. What is the present value if payments are made monthly instead of annually?
5. How does inflation affect the time value of money?

**Tip:** Always compare the present value of payments to any lump sum offer to make informed financial decisions.

A financial company that advertises on television will pay you $46,000 now for annual payments of $8,000 that you are expected to receive for a legal settlement over the next 8 years. Use Exhibit 1-D.
What is the present value of the annual payments if you estimate the time value of money at 9 percent?
Note: Round your PVA factor to 3 decimal places and final answer to the nearest whole dollar.
Should you accept this offer?

Learn how to calculate the present value of an $8,000 annual payment received over 8 years with a 9% interest rate. This step-by-step solution uses the Present Value of Annuity formula and discusses whether to accept a lump sum offer of $46,000. Suitable for finance and business students.

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