Exponential functions of time share one characteristic: the growth rate is proportional to the current value. Anyone who’s studied differential equations can tell you that exponential functions are synonymous with that statement.
You would be right if interest wasn’t compounded. If we only earned interest on what we initially put in, our money would grow linearly, not exponentially, because we’re not earning interest on our interest payments. But with compound interest, the amount our money grows is equal to some constant (the interest rate) times the total amount of money in our account, previous interest payments and all. Growth rate is proportional to the present amount. That’s
exponential, and eventually it will grow out of control. Though, if you were to calculate how long it would take, you’d realize you’d be long dead thanks to the incredibly slow start.
Exponential functions of time share one characteristic: the growth rate is proportional to the current value. Anyone who’s studied differential equations can tell you that exponential functions are synonymous with that statement.
You would be right if interest wasn’t compounded. If we only earned interest on what we initially put in, our money would grow linearly, not exponentially, because we’re not earning interest on our interest payments. But with compound interest, the amount our money grows is equal to some constant (the interest rate) times the total amount of money in our account, previous interest payments and all. Growth rate is proportional to the present amount. That’s exponential, and eventually it will grow out of control. Though, if you were to calculate how long it would take, you’d realize you’d be long dead thanks to the incredibly slow start.
That makes a lot of sense, actually.