A sailboat costs 20842$ You pay 10% down and amortize the rest with equal monthly payments over a 14 ​-year period. If you must pay 6.6% compounded​ monthly, what is your monthly​ payment? How much interest will you​ pay?

Answer 1

To calculate the monthly payment, we need to determine the loan amount after the down payment.

10% of $20842 is (10/100) * $20842 = $2084.2

The loan amount is $20842 - $2084.2 = $18757.8

To determine the monthly payment, we can use the formula for the monthly payment on an amortizing loan:

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

Where:
P = monthly payment
r = monthly interest rate
PV = loan amount
n = number of months

The monthly interest rate is (6.6/100) / 12 = 0.0055

The loan amount is $18757.8
The number of months is 14 * 12 = 168

P = (0.0055 * $18757.8) / (1 - (1 + 0.0055)^(-168))

Using a calculator, we find that P ≈ $168.66

Therefore, your monthly payment will be approximately $168.66.

To determine the total interest paid over the 14-year period, we can subtract the loan amount from the total amount paid.

Total amount paid = $20842 (initial cost of the sailboat) + ($168.66/month * 168 months)

Total amount paid = $20842 + (168.66 * 168)

Total amount paid = $20842 + $28360.88

Total amount paid = $49202.88

Interest paid = Total amount paid - Loan amount

Interest paid = $49202.88 - $18757.8

Interest paid = $30445.08

Therefore, you will pay approximately $30445.08 in interest over the 14-year period.