A successful businessman is selling one of his fast food franchises to a close friend. He is selling the business today for $2,259,000.00. However, his friend is short on capital and would like to delay payment on the business. After negotiation, they agree to delay 5.00 years before the first payment. At that point, the friend will make quarterly payments for 17.00 years. The deal calls for a 6.36% APR “loan” rate with quarterly compounding. What quarterly payment will the friend make on the loan?

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Answer format: Currency: Round to: 2 decimal places.

To find the quarterly payment that the friend will make on the loan, we will use the formula for the present value of an annuity, as the loan can be considered an annuity with quarterly payments over a period of time.

### Given:
- Present value $ PV $ (the loan amount) = \$2,259,000
- Annual interest rate $ r $ = 6.36%
- Payments are made quarterly, so we need the quarterly interest rate:  
  $ r_{quarterly} = \frac{6.36\%}{4} = 0.0159 $ or 1.59%
- The number of quarters for the loan:  
  $ n = 17 \text{ years} \times 4 = 68 \text{ quarters} $
- The payments start after 5 years, so the present value is based on when payments start.

### Step 1: Adjust the loan for the 5-year delay.
The loan amount is delayed by 5 years, or 20 quarters, so we first need to adjust the present value to when the payments start. This is done by discounting the present value back to the point when the payments begin:

\[
PV_{\text{adjusted}} = \frac{PV}{(1 + r_{quarterly})^{20}}
\]

### Step 2: Use the formula for the annuity payment:
The formula for the quarterly payment $ P $ is:

\[
P = \frac{PV_{\text{adjusted}} \cdot r_{quarterly}}{1 - (1 + r_{quarterly})^{-n}}
\]

Let’s calculate this.The quarterly payment that the friend will need to make is approximately **\$39,822.15**.

Would you like further details on the calculation or any other questions? 

Here are 5 related questions:
1. How would the quarterly payment change if the interest rate were higher or lower?
2. What if the delay in payments was longer than 5 years?
3. How much interest will the friend end up paying over the 17 years?
4. What would the total cost of the loan be including interest?
5. How does quarterly compounding affect the loan compared to annual compounding?

**Tip:** Always account for compounding frequency when calculating loan payments, as it significantly affects the total payment amount.

A successful businessman is selling one of his fast food franchises to a close friend. He is selling the business today for $2,259,000.00. However, his friend is short on capital and would like to delay payment on the business. After negotiation, they agree to delay 5.00 years before the first payment. At that point, the friend will make quarterly payments for 17.00 years. The deal calls for a 6.36% APR 'loan' rate with quarterly compounding. What quarterly payment will the friend make on the loan?

Learn how to calculate the quarterly loan payment for a business franchise sale delayed by 5 years, with 6.36% APR and quarterly compounding. This problem uses key financial concepts like loan amortization and the time value of money. Perfect for finance students or anyone dealing with complex loan scenarios.

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