Question

Your bank account pays interest with an EAR of 4 %. What is the APR quote for this account based on semiannual​ compounding? What is the APR with monthly​ compounding?​ (Note: Be careful not to round any intermediate steps less than six decimal​ places.)

Answer 1

Answer:

APR would be 3.9607805% compounded semiannually

APR would be 3.9284877% compounded monthly

Explanation:

We calcualte consider these rates should be inancially equivalent to an equivalent rate of 4% annually.

The semiannual compounding will capitalize two times:

$(1+APR/2)^2 = 1+EAR\\(\sqrt{1.04} -1) \times 2 = 0.039607805$

The monthly will capitalize 12 times per year:

$(1+APR/12)^12 = 1+EAR\\(\sqrt[12]{1.04} -1) \times 12 = 0.039284877$