Find the effective rate corresponding to the given nominal rate.

Question

Find the effective rate corresponding to the given nominal rate. (Use a 365-day year. Round your answer to two decimal places.)

4%/year compounded quarterly

____% /year

I would appreciate any help on this problem. Thank you in advance.

Answer 1

The effective rate equation is:

E = [ 1 + ( R ⁄ n )ⁿ ] - 1

E = effective rate

R = nominal (annualized) rate

n = # of periods per year (# of times compounded in a year)

For this problem,

R = 4% = 0.04

n = 4 (Since interest is compounded quarterly, the number of days in a year really doesn't matter. Quarterly means 4 times per year.)

R ⁄ n = 0.01

E = (1.01)⁴ - 1 = 0.0406 = 4.06%