The bank offers you a 8% continuously compouding interest rate. If the bank offers you an equivalent interest rate compounded quarterly, what will that interest

Question

The bank offers you a 8% continuously compouding interest rate. If the bank offers you an equivalent interest rate compounded quarterly, what will that interest rate be?

 

 

Answer 1

Continuously compounded interest formula:  A = Pe^rt

Compound interest:  A = P(1+r/n)^nt

 

Pe^.08t = P(1+r/4)^4t

e^.08t = (1+r/4)^4t

ln(e^.08t) = ln(1+r/4)^4t

.08t = (4t)ln(1+r/4)

.02 = ln(1+r/4)

 

e^.02 = 1 + r/4

r/4 = e^.02 - 1

r = 4(e^.02 -1)

r = .0808

r = 8.08%