323.13
13.The Penn State Alumni Association keeps asking me to buy a lifetime membership at a cost of $500. The annual membership fee is $25 and my next one is due in a year.
You don’t have to answer the question of how old I am or how long I will live to answer this question. Even if I’m immortal (like the Highlander), the lifetime membership is a bad deal. Look at it this way: it would be cheaper for me to fund a perpetuity of annual membership dues than to pay the $500 for the lifetime membership. Here’s how: if I can earn 8% on my money, it would cost me $312.50 ($25/.08)to fund a perpetuity of $25 every year to automatically pay my annual fee (every year the $312.50 would earn 8% interest = $25).
Again, you don’t have to assume anything about my life expectancy. Even if I live forever, the lifetime membership is still a bad deal. I could set-up a perpetuity of cash flows that grows to keep-up with the increase in the membership fee. Here’s how much it would cost:
$25/(0.08-0.025) = $454.55. The interest that my larger initial investment would earn allows it to keep up with the increase in the necessary annual cash flow.