With simple interest, we’re stuck in a car going the same speed: /year, or 50 mph.
In other cases, our rate may change, like a skydiver: they start off slow, but each second fall faster and faster.
After n periods you have: This formula works as long as “r” and “n” refer to the same time period.
Simple interest keeps the same trajectory: we earn “P*r” each year, no matter what ($50/year in this case).
That straight line perfectly predicts where we’ll end up.
Like Roman numerals and hieroglyphics, our first system “worked” but wasn’t quite ideal. But wait a minute — after our June payout we’d have 106 gold in July, and yet earn only 6 during the rest of the year?
In the beginning, you might have had 100 gold coins and were paid 12% per year (percent = per cent = per hundred — those Roman numerals still show up! Are you saying 100 and 106 earn the same amount in 6 months?
There’s no trickery because there’s no compounding — interest can’t grow.