Question

You would like to vacation in Hawaii for one week each year.
You can buy a time share for a vacation home in Hawaii for $18,500 today and a maintenance fee of $600 per year starting next year. You expect to sell the time share in 10 years for $19,000 .
Alternatively you can just pay for the week vacation each year (starting next year). Each year will cost you $1,500 .

If your investments earn 5% per year (compounded annually) which alternative is cheaper and by how much in present value terms?

Group of answer choices

Buy the time share it will save you $120

Pay each year it will save you $122

Pay each year it will save you $110

Buy the time share it will save you $114

please work out

Answer 1

PV of Costs for vacation home in first alternative =Investment in time Share +PV of Maintenance fee
=18500+600*((1-(1+5%)^-10)/5%)-19000/(1+5%)^10 =11468.69
PV of Cost of Week vacation =PV of Yearly payments =1500*((1-(1+5%)^-10)/5%)=11582.60

The second alternative (weekly vacation plan is costlier by =11582.60-11468.69 =113.91 or 114

option Hence buy the time share it will save you 114