Question

7. What is the effective annual interest rate for a bank account that pays a continuously compounded interest rate of 8%?

Answer 1

Continuous compunded intrest rate formula is (assumung that the interest is being compounded on monthly bassis and the tenure of the deposit is 1 year)

P(t) =P_0*^ert

P(t) = Value of time t

P₀ = Original Principal sum

r = Nominal annual intrest rate

t = Length of the time to which intrest is applied

r = 0.08/12 (i.e. per month intrest rate) = 0.0066667

t = 12 months

P = Lets assume $100

p(t) = 100*e^{0.0066667(12)}

^{p(t) = 108.33}

^{Effective rate of interest = (108.33-100)/100 = 8.33%}