Falco Inc. financed the purchase of a machine with a loan at 4.88% compounded monthly. This loan will be settled by making payments of $7,200 at the end of every month for 9 years.

a. What was the principal balance of the loan?

To find the principal balance of the loan, we need to calculate the present value of the loan payments.

The formula for the present value of an ordinary annuity is:

PV = PMT * [(1 - (1 + r)^(-n)) / r]

Where:
PV = Present value
PMT = Payment amount
r = Interest rate per period
n = Number of periods

In this case, the payment amount (PMT) is $7,200, the interest rate (r) is 4.88% compounded monthly (which is equivalent to 0.0488/12 = 0.0040667 per month), and the number of periods (n) is 9 years * 12 months/year = 108 months.

Plugging these values into the formula:

PV = $7,200 * [(1 - (1 + 0.0040667)^(-108)) / 0.0040667]

Using a financial calculator or spreadsheet software, we can find the present value:

PV ≈ $7,200 * [(1 - (1 + 0.0040667)^(-108)) / 0.0040667] ≈ $608,723.52

So, the principal balance of the loan is approximately $608,723.52.

To find the principal balance of the loan, we need to calculate the present value of the monthly payments.

The formula to calculate the present value of an ordinary annuity is:

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

Where:
PV is the present value (principal balance)
P is the monthly payment
r is the interest rate per period
n is the number of periods

In this case, the monthly payment (P) is $7,200, the interest rate (r) is 4.88% per period (which is compounded monthly), and the number of periods (n) is 9 years * 12 months/year = 108 months.

Now, let's calculate the principal balance:

PV = $7,200 * (1 - (1 + 0.0488/12)^(-108)) / (0.0488/12)
PV = $7,200 * (1 - (1.00407)^(-108)) / (0.00407)
PV ≈ $580,004.54

Therefore, the principal balance of the loan is approximately $580,004.54.