Continuous Compounding Many banks advertise that they compound interest continuously, meaning that the amount of money A(t) in an account satisfies the DE A′ = rA, where r is the annual interest rate and t is time in years.
(a) Show that an interest rate of 8% compounded continuously gives an effective annual interest rate of 8.329%; that is, the yield is the same at 8% compounded continuously as at 8.329% compounded annually.
(b) Show that an interest rate of r, compounded continuously, gives an effective annual interest rate of er − 1.
(c) Compare the effective annual interest rates for 8% compounded continuously and 8% compounded daily.
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