Time-share sales provide an opportunity for vacationers to own a resort condo for 1 week (or more) each year forever. The owners may use their week at their own condo or trade the week and vacation elsewhere. Timeshare vacation sales usually require payment in full or financing through the time-share company, and interest rates are usually in the 13% to 18% range. Suppose the cost to buy a 1-week time share in a 3-bedroom condo is $21,773. Also suppose a 10% down payment is required, with the balance financed for 15 years at 17.5%, compounded monthly. (Round your answers to the nearest cent.)
(a) Find the monthly payment.
$ 1
(b) Determine the total cost over the life of the loan.
$ 2
(c) Suppose maintenance fees for this condo are $400 per year. Find the annual cost of the condo over the life of the loan. Assume that the annual maintenance fees remain constant.
$ 3
(d) Use (c) and the 10% down payment to determine the average annual cost for having this vacation condo for 1 week over the life of the loan.
$ 4
Don’t know
To find the monthly payment for the time-share condo, we can use the formula for the monthly payment on a loan with monthly compounding:
P = (r * PV) / (1 - (1 + r)^(-n))
Where:
P = monthly payment
r = monthly interest rate
PV = present value (loan amount)
n = number of monthly payments
(a) First, let's calculate the monthly payment.
Given:
Loan amount (PV) = $21,773
Down payment = 10% of PV = 0.1 * $21,773 = $2,177.30
Finance amount = PV - Down payment = $21,773 - $2,177.30 = $19,595.70
Interest rate (r) = 17.5% per year = 17.5 / 100 / 12 = 0.01458 per month
Number of monthly payments (n) = 15 years * 12 months/year = 180
Using the formula, we can substitute the values:
P = (0.01458 * $19,595.70) / (1 - (1 + 0.01458)^(-180))
P ≈ $269.20
Therefore, the monthly payment for the time-share condo is approximately $269.20.
(b) To find the total cost over the life of the loan, we can multiply the monthly payment by the number of monthly payments.
Total cost = P * n
Total cost = $269.20 * 180 ≈ $48,456
Therefore, the total cost over the life of the loan is approximately $48,456.
(c) The annual cost of the condo over the life of the loan includes the annual maintenance fees.
Annual maintenance fees = $400
Since the loan term is 15 years, the number of years is 15.
Annual cost of the condo over the life of the loan = Annual maintenance fees * Number of years
Annual cost of the condo over the life of the loan = $400 * 15 = $6,000
Therefore, the annual cost of the condo over the life of the loan is $6,000.
(d) To determine the average annual cost for having this vacation condo for 1 week over the life of the loan, we need to divide the total cost over the life of the loan by the number of years.
Average annual cost = Total cost / Number of years
Average annual cost = $48,456 / 15 ≈ $3,230.40
Therefore, the average annual cost for having this vacation condo for 1 week over the life of the loan is approximately $3,230.40.