You love to swim and are considering whether to install a pool in your house or just have a membership to a private swimming pool. To install a pool will cost you $20,000 today and $200 per month for maintenance costs (the maintenance costs start next month and go for 20 years).
If you join the private swimming pool, it will cost you $500 per month, starting next month, for 20 years.
If your investments earn 5% APR (compounded monthly) which alternative has cheaper in present value terms and by how much?