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# (Compound interest) If one invests an amount A 0 with interest rate r compounded annually, after one year it will be worth A 0 (1 +r).

(Compound interest) If one invests an amount A0 with interest rate r compounded annually, after one year it will be worth A0(1 +r).

(a) Find an expression for A(t), the value of the investment after t years.

(b) Suppose that the investment is compounded n times per year. Then, assuming the investment rate during each period is r/n, find an expression for A(t). (Make sure the case n= 1 is the same as your answer to part (a)!)

(c) Suppose that A0= 100 and that r= 0.03. Compare the values of A(t= 1 year) for annual compounding and daily compounding (365 times per year)