Question

Find the effective rate corresponding to the given nominal rate. (Round your answer to the nearest hundredth of a percentage point.)
(a) 4%/year, compounded quarterly

? %

(b) 3%/year, compounded monthly

? %

Answer 1

let the effective rate in each case be i

a)
so (1+i)^1 = 1.-1^4
1+i = 1.040604
i = .040604 = 4.06%

f)
3% compounded monthly --- monthly rate of .0025

1+i = 1.0025^12 = 1.0304059..
rate = .0304 or 304%

Answer 2

(1+r)^12 = 1.03
1+r = (1.03)^1/12
1+r = 1.00246627
r = 0.00246627
r % = .247 % monthly