The bank offers you a 6% 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 6% continuously compounding interest rate. If the bank offers you an equivalent interest rate compounded quarterly, what will that interest rate be (use 3 significant figures and express as a percent)?

Answer 1

Continuous compounding: A=Pe^rt

Quarterly compounding: A=P(1+r/n)^nt

 

Set these equal to one another:

Pe^rt=P(1+r/n)^nt

 

The P's will cancel and we can plug in the information given:

e^.06t=(1+r/4)^4t

 

The t in the exponent will cancel on both sides:

e^.06=(1+r/4)⁴

 

1.0618=(1+r/4)⁴

 

Take the 1/4 exponent of both sides:

1.01511=(1+r/4)

 

Simplify:

r=.06045

r=6.045%