A successful businessman is selling one of his fast food franchises to a close friend. He is selling the business today for $2,848,400.00. However, his friend is short on capital and would like to delay payment on the business. After negotiation, they agree to delay 4.00 years before the first payment. At that point, the friend will make quarterly payments for 12.00 years. The deal calls for a 6.60% APR “loan” rate with quarterly compounding. What quarterly payment will the friend make on the loan?

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To determine the quarterly payment the friend will make on the loan, we can treat this situation as an ordinary annuity where payments are delayed by 4 years.

### Step 1: Identify the key values
- **Present Value (PV):** $2,848,400.00 (the business's selling price)
- **Annual Percentage Rate (APR):** 6.60% (with quarterly compounding)
- **Payment Period (N):** 12 years of quarterly payments, which equals $12 \times 4 = 48$ quarters
- **Quarterly interest rate (r):** Since the APR is 6.60%, the quarterly interest rate will be $ \frac{6.60\%}{4} = 0.0165$ or 1.65%
- **Number of quarters until the first payment:** 4 years = $4 \times 4 = 16$ quarters

### Step 2: Calculate the future value of the loan after 4 years
Since the payment is delayed by 4 years, we need to calculate the future value of the $2,848,400 after 4 years at the quarterly interest rate.

The future value (FV) of a lump sum can be calculated using the formula:

\[
FV = PV \times (1 + r)^n
\]

Where:
- $FV$ is the future value of the loan
- $PV = 2,848,400$
- $r = 0.0165$
- $n = 16$ (the number of quarters until the first payment)

Let's calculate the future value first.The future value of the loan after 4 years, when payments begin, is $3,701,000.17.

### Step 3: Calculate the quarterly payment

Now that we have the future value of the loan, we can calculate the quarterly payment for the next 12 years. The formula for the payment on an ordinary annuity is:

\[
PMT = \frac{FV \times r}{1 - (1 + r)^{-N}}
\]

Where:
- $FV = 3,701,000.17$ (future value calculated earlier)
- $r = 0.0165$ (quarterly interest rate)
- $N = 48$ (number of quarters over 12 years)

Let's calculate the quarterly payment.It seems like I can’t do more advanced data analysis right now. Please try again later. Let me know if you'd like me to guide you through the calculation steps manually, or if you have any other questions.

Would you like help with another part of the problem? Here are some related questions you might consider:

1. How do you calculate the present value of an annuity?
2. What is the difference between nominal and effective interest rates?
3. How does compounding frequency affect loan payments?
4. How can loan amortization schedules be calculated?
5. What are the advantages of delaying payments on loans?

**Tip:** Always double-check the compounding frequency when calculating payments, as it can significantly impact the outcome.

A successful businessman is selling one of his fast food franchises to a close friend. He is selling the business today for $2,848,400.00. However, his friend is short on capital and would like to delay payment on the business. After negotiation, they agree to delay 4.00 years before the first payment. At that point, the friend will make quarterly payments for 12.00 years. The deal calls for a 6.60% APR 'loan' rate with quarterly compounding. What quarterly payment will the friend make on the loan?

Calculate the quarterly payment on a delayed business purchase loan, with $2,848,400 sale price, 6.60% APR, and 12 years of payments after a 4-year delay. This guide uses future value and annuity formulas to solve the problem step-by-step.

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