6. Barry bought a boat two years ago and at that time paid a down payment of $10000 cash. Today he must make the second and final payment of $7500, which includes the interest charge on the balance owing. Barry financed this purchase at 13.7%/a. Determine the purchase price of the boat?
[1 + (2 * .137)] * (p - 10000) = 7500
To determine the purchase price of the boat, we first need to calculate the interest charged on the balance owing.
The interest charge is calculated using the formula:
Interest = Principal * Rate * Time
Let's break down the given information:
Principal (balance owing) = $7,500 (second and final payment)
Rate = 13.7%/a (annual interest rate)
Now, we need to know the time. You mentioned that Barry bought the boat two years ago and made a down payment of $10,000 at that time. Since the second and final payment is being made today, we assume that the loan term is two years.
Next, we calculate the interest charge:
Interest = $7,500 * 13.7%/a * 2 years
Interest = $7,500 * 0.137 * 2
Interest = $2,055
Now that we have the interest charged, we can calculate the total amount paid for the boat:
Total amount paid = Principal + Interest
Total amount paid = $7,500 + $2,055
Total amount paid = $9,555
Finally, we can determine the purchase price of the boat:
Purchase price = Total amount paid + Down payment
Purchase price = $9,555 + $10,000
Purchase price = $19,555
Therefore, the purchase price of the boat is $19,555.