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To solve this problem, let's go through the key steps:

1. **Identify the future value (FV) of Pete's Real Estate if he holds onto it** (compounded semiannually at 8% for 6 years).
2. **Compare it to the present value (PV) of the offered $88,000 if invested at 6% compounded quarterly**.
3. **Determine if the offer is worth accepting based on the required future value Pete would need.**

### Step-by-Step Solution

#### Step 1: Calculating the Future Value of Pete's Real Estate
The current value of the business is $83,000, expected to grow at 8% per year, compounded semiannually.

- **Formula**: $ FV = PV \times (FVIF) $
- **Interest rate per period**: Since the compounding is semiannual, the rate per period is $ \frac{8\%}{2} = 4\% $.
- **Number of periods**: Since it's compounded twice a year for 6 years, $ n = 6 \times 2 = 12 $.

Using **Table 1** (Future Value Interest Factor), find $ FVIF(4\%, 12) $.

From the table, the **FVIF(4%, 12) = 1.6010**.

So, the future value calculation:
\[
FV = 83,000 \times 1.6010 = 132,883
\]

#### Step 2: Calculating the Present Value of the $88,000 Offer
If Pete invests the $88,000 at a 6% annual rate, compounded quarterly, we need to determine what future value this would need to reach to be worth selling.

- **Formula**: $ PV = FV \times (PVIF) $
- **Interest rate per period**: $ \frac{6\%}{4} = 1.5\% $.
- **Number of periods**: Compounded quarterly for 

Pete’s Real Estate is currently valued at $83,000. Pete feels the value of his business will increase at a rate of 8% per year, compounded semiannually for the next 6 years. At a local fund-raiser, a competitor offered Pete $88,000 for the business. If he sells, Pete plans to invest the money at 6% compounded quarterly. What price should Pete ask?

Solve Pete’s Real Estate valuation problem using compound interest calculations. Learn how to calculate future value with an 8% interest rate compounded semiannually and compare it to the present value of an $88,000 offer with a 6% rate compounded quarterly. Suitable for college-level students.

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