A guy buys a car for $29,000 and finances it with a four year, 7% APR with monthly payments and compounding. How much of his third payment goes toward repaying principal?

To calculate the amount of the third payment that goes toward repaying principal, we need to use the loan formula and amortization schedule.

First, let's break down the given information:
- Principal Amount (car price): $29,000
- Loan Term: 4 years (48 months)
- Annual Percentage Rate (APR): 7%
- Payment Frequency: Monthly

To calculate the monthly payment amount, we can use the loan formula:

P = (r * PV) / (1 - (1 + r)^(-n))

Where:
P = Monthly Payment
r = Monthly Interest Rate
PV = Present Value (Principal Amount)
n = Total Number of Payments

Plugging in the values, we have:

PV = $29,000
n = 4 years * 12 months = 48 months
r = (7% / 100) / 12 = 0.00583 (monthly interest rate)

P = (0.00583 * 29000) / (1 - (1 + 0.00583)^(-48))

Calculating this formula gives us the value of P, which represents the monthly payment.

Next, let's create an amortization schedule, which shows the breakdown of each payment into principal and interest:

| Payment | Payment Amount | Principal Payment | Interest Payment | Remaining Balance |
|---------|----------------|-------------------|------------------|------------------|
| 1 | P | - | - | $29,000 |
| 2 | P | - | - | - |
| 3 | P | ? | ? | - |
| ... | ... | ... | ... | ... |
| 48 | P | - | - | $0 |

In the amortization schedule, we will calculate the principal payment and interest payment for each payment.

The principal payment for the third payment can be calculated using the loan formula with an adjusted remaining balance:

Principal Payment = P - (Remaining Balance * Monthly Interest Rate)

Once we have calculated the principal payment, we can subtract it from the monthly payment to find the interest payment.

Therefore, to determine the amount of the third payment that goes toward repaying principal, you need to calculate the values using the loan formula and create an amortization schedule.