eljay
Well-known member
compounding interest is the result of integrating the interest rate over time.
suppose that interest is continuously compounded at the rate of r for time from 0 to x. then the compounding function is exp(rt) - proof of why is left for later in university (it's the limit of an integrated riemann sum of discretely compounded interest rates).
so how much does one dollar cost from time 0 to x?
integral of exp(rt)dt from 0 to x = exp(rx) - exp(r0) = exp(rx)-1.
see? calculus is useful.
suppose that interest is continuously compounded at the rate of r for time from 0 to x. then the compounding function is exp(rt) - proof of why is left for later in university (it's the limit of an integrated riemann sum of discretely compounded interest rates).
so how much does one dollar cost from time 0 to x?
integral of exp(rt)dt from 0 to x = exp(rx) - exp(r0) = exp(rx)-1.
see? calculus is useful.
If they only taught people about compounding interest more than calculus and derivatives in high school, it'd be a much different world.
anyway, back on topic.
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