math & finance
posted by Thara on .
A bank offers a rate of 5.3% compounded semi-annually on its four year GICs(Guaranteed Investment Certificates). What monthly and annually compounded rates should it quote in order to have the same effective interest rate at all three nominal rates?
See double post:
first calculate the annual equivalence
(1+.053/2)^2 = 1.0537 ergo, the equivalent annual rate is 5.37%
Let the monthly equivalent rate be x.
So (1+x/12)^12 = 1.0537
12ln(1+x/12) = ln(1.0537) = .0523078
ln(1+x/12) = .00435898
(1+x/12) = e(.00435898) = 1.0043685
x/12 = .0043685
x = .05242
annual rate is 5.242%