How might interest be described as a problem of sequences?
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Ok, what's the formula for a geometric series?
And what's the formula for compound interest?
How do they compare?
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the principle P grows every time period by (1+i). This is just like the growth rate in a geometric series of r, where r > 1.
In a geometric series, suppose a = 100 and r = 1.1. Then after one step, a has grown to
ar = 110
One more step and its
Now start with $100 and grow it at 10%. After one time period, the $100 has grown to
One more time period and we're at
The ratio of the value of the principle one time step later is a constant and that constant is 1+i where i is the interest rate. This is just like a geometric series where the ratio of successive terms is constant.