How to get rich quick?

Question

When John learned that company 'Galactic Stardust'
offers tours on space cruisers travelling 0.99c for just
$500 a day (proper time), he decided to sell part of his
$1,000,000 portfolio of bonds earning 10% a year and
purchase a tour ticket. What will be effective proper
interest rate on his entire fortune ($1M), if he wants to
have maximum amount of money upon his return?

"Can you describe the problem a little better?"

Wonderful! Tthe first prospective customer knocks on the door.

Answer 1

The chief difficulty of doing this problem is first figuring out exactly what is the problem being posed. I've decided that the part that got left out is that John can buy any number of days travelling at 0.99c, so what's the maximum money he can find in his fund when he returns? We know that it costs $182,500 a proper year to travel at 0.99c, so that his original $1 mil account will have grown as per the following equation, where x is number of proper years to be determined:

(1,000,000 - 182,500 x) (1.1)^(x/√(1-(0.99)²))

The maximum is $4,027,760 after 3.99937 years of travel, which is just about 41.67% rate of return per proper year.

Paradoxically, this is not the maximum rate of return in proper time. It's 63.74% if he leaves for only 1 day. It drops to 0% if he leaves for 5.479 proper years, because the space fare would have cost him $1,000,000.

Answer 2

Can you describe the problem a little better? I'm not getting what's going on here.

Your additional details aren't illuminating. Can you help describe what the question really is?