Here you go with out compounding interest. I used your numbers $22K for average initial purchase and while I don't agree at all the developer willing to buy back at 50% initial purchase price. I did not compound annual interest in the end the renter is way better off than the developer buyer. Remember the renter will still have $22K in the bank while the Buyer under your scenario would get $11K Back.
Here are my spreadsheets for Rent vs. Own and Investment vs. Own at the average costs given by ARDA (believe it or not, my company has packages of similar price and lower maintenance).
First is Rent vs. Own:
Assumptions:
1 week in a hotel vs. a 1 week timeshare deed
Hotel Rents are assumed to be $220/night for a 1-bedroom luxury resort at a popular destination, which is argued to be fair in comparison to the average US hotel ADR of $140/night for a studio.
Hotel taxes are assumed to be 15%, slightly above the national average of 13.7% to account for the popular destinations offered by timeshare resorts.
We will use a Net Present Value analysis to account for the time value of money, and apply a 2% discount rate to all future cash flows. 2% is argued to be fair as the traditional metric for this sort of analysis is the 3-month T-bill, which is currently at 2.4% but has been close to zero for most of the last decade, as seen by the chart below.
Hotel ADR inflation is assumed to be 3.7%, the estimated rate in 2018 (I do not try to manipulate you into believe it is 7-8% as some reps do).
Maintenance fee inflation is assumed to be 2.5%.
Deed equity value of the timeshare deed is set at 50% of retail price, which is assumed to appreciate at 4% annually
Initial Investment in the timeshare deed is set to depreciate in purchasing power at the discount rate
First Day Incentive value is assumed to be equal to the discounted cost of renting 3 weeks over the next 3 years
And here is the chart for a savvy negotiator that is able to command 5 weeks worth of First Day Incentives:
And just for fun, here's a chart with 3 weeks FDI and the deed set to ZERO equity value:
Timeshare wins the numbers handily in all cases.
Now, Investment vs. Own:
Assumptions:
The equivalent amount of capital to purchase a deed was placed into an Investment Fund, assumed to appreciate at 5% per year.
We have again used an NPV analysis that discounts all future cash flows at the assumed rate of 2%
Hotel rent was assumed to be $220/night + 15% taxes, appreciating at 3.7% annually.
The capital gains of the investment only purchase 3.7 nights in the 1st year, and less each successive year due to inflation. Because the compared plans are for 7 days, it is assumed that additional money is spent each year to bring the number of nights up to 7.
Maintenance fee inflation is assumed to be 2.5%
Deed equity value of the timeshare deed is set at 50% of retail price, which is assumed to appreciate at 4% annually
Initial Investment in the timeshare deed is set to depreciate in purchasing power at the discount rate
First Day Incentive value is assumed to be equal to the discounted cost of renting 3 weeks over the next 3 years
Timeshare again wins the numbers vs. an investment fund.