Question

Relate the compound interest or any economical formula to calculus, whether it is related to model of exponential growth/decay, derivatives, etc. Use simple math/english.

Answer 1

Compound interest works just like any other exponential function.

An exponential function f(x) is in the form of y^x and if y > 1, then f(x) grows exponentially as x increases and if y<1, f(x) decays exponentially.

Now look at the formula for compound interest (actually compounded value of a sum including compound interest)

if P = pricincipal amount

r = rate of interest per period

t = number of periods

then Accumulated amount = P*(1+r)^t

the part (1+r) is the y we saw in the exponential function example and the t is x in the example. And the accumulate amount also grow exponentially as t increases.