Let's say the APR is 5%. That means you get 5% of your balance back every year. The $100 balance would get $5 back, the $500 balance would get $25 back, and the $1000 balance would get $50 back. Therefore, all of the balances would take the same amount of time to double, and it would take all of them 20 years.
$5*20 years=$100
$25*20 years=$500
$50*20 years=$1000
