Compound interest is the easy part. Lets see if some one can explain using a practical numerical example.
1) I have a 100,000 BC balance
2) I am lucky[ fulfilling the 8hrs, unlocked reqmt, etc] and get a stake of 10,000 BC
To keep thing,s simple I get no further stake for weeks.
Explain using said numbers what happens to that 10000 BC incl. interest collected, over the period of the stake. Is the period of the stake random as well ?
to get you started 1% pa of 10000 BC is 100 BC per year or 0.28 BC/day in interest.
From the source:
int64 nSubsidy = nCoinAge * COIN_YEAR_REWARD * 33 / (365 * 33 + 8 );
nCoinAge is days. For the age of your coin you get 1% * coinage / days in a year.
So to put in numbers.
You have 100,000 coins that are all 8 hours old and generate a stake. You get 100000 * .01 * .33 / 365 = 0.904109.
You now have 100000.904109
Next time you wait 5 days before you generate a stake.
100000.904109 * .01 * 5 / 365 = 13.69875
Now you have 100014.602859
Next time you wait 90 days
100014.602859 * .01 * 90 / 365 = 246 .611348
Now you have 100261.214207
Next time you wait the rest of the year
100261.214207 * 0.01 * 269.66 /365 = 740.724356
Now you have 101001.938563
Or just a bit over 1% annually.
This will always come out to a bit over 1% annually because the coin age continues to grow until the coins stake. The period they will actually stake is random, but irrelevant because the reward uses coin age. But the incentive to keep your wallet open and generating POS (and therefore securing the network and moving transactions) is that the more frequent they stake, though you get a smaller reward in each interval, the interest will be compounded more often.