John Sullivan bought a new Brunswick boat for $17,000. He made a $2,500 down payment on it. The bank's loan was for 60 months. Finance charges totaled $4,900. His monthly payment is:

Question

Quizplus · Accepted Answer

First, we need to find the amount of the loan. 
Loan = Total cost of the boat - Down payment 
Loan = $17,000 - $2,500 
Loan = $14,500

Next, we need to add the finance charges to the loan amount. 
Total amount financed = Loan + Finance charges 
Total amount financed = $14,500 + $4,900 
Total amount financed = $19,400

Now, we can use the formula for the monthly payment on a loan:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

Where: 
M = Monthly payment 
P = Principal (amount financed) 
i = Monthly interest rate 
n = Number of payments

First, we need to find the monthly interest rate. We know the loan is for 60 months, so:

n = 60

To find the monthly interest rate, we need to divide the annual interest rate by 12:

Annual interest rate = Finance charges / Loan 
Annual interest rate = $4,900 / $14,500 
Annual interest rate = 0.3379 or 33.79%

Monthly interest rate = 33.79% / 12 
Monthly interest rate = 0.02816

Now, we can plug in the values:

M = $19,400 [ 0.02816(1 + 0.02816)^60 ] / [ (1 + 0.02816)^60 – 1]

M = $19,400 [ 0.02816(1.02816)^60 ] / [ (1.02816)^60 – 1]

M = $19,400 [ 0.02816(2.47852) ] / [ 2.47852 – 1]

M = $19,400 [ 0.0691 ] / 1.47852

M = $1,342.24 / 1.47852

M = $907.51

So the monthly payment is $907.51, which is closest to choice B, $323.33. However, this answer is not correct, so we need to check our work.

We made a mistake in using the formula. The formula we used is for a fully amortized loan, where the interest and principal are paid off over the term of the loan. However, this loan has a balloon payment at the end, where the entire remaining balance is due.

To find the monthly payment, we need to use the following formula:

M = (P * r) / (1 – (1 + r)^-n)

Where: 
M = Monthly payment 
P = Principal (amount financed) 
r = Monthly interest rate 
n = Number of payments

We already calculated the total amount financed as $19,400.

r = 0.02816 (from our previous calculation)

n = 60 (the number of payments)

M = ($19,400 * 0.02816) / (1 - (1 + 0.02816)^-60)

M = ($547.84) / (1 - 0.22199)

M = ($547.84) / (0.77801)

M = $703.60

So the correct answer is $703.60, which is closest to choice B, $323.33. Therefore, none of the choices are correct.

John Sullivan Bought a New Brunswick Boat for $17,000