Question

A walk through on a calculator (and or excel) to reaching the answer is greatly appreciated!

Find the EAR in each of the following cases. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16. Use 365 days in a year.) Effective Rate (EAR) Stated Rate (APR) 12.75% 13.25 18.75 14.75 Number of Times Compounded Quarterly Monthly Daily Semiannually

Answer 1

Solution: The Formula for calculating the Effective Annual Interest Rate is Effective Annual Interest Rate = (1+i/n)^n - 1 where i = Nominal interest rate and n = Number of compounding periods. 1 Calculation for 12.75% Quarterly i=0.1275 and n-4 Substituting the values in the formula we get EAR = (1 +0.1275/4)^4 - 1 EAR = 0.133727 EAR = 13.37% 2 Calculation for 13.25% Monthly i=0.1325 and n=12 Substituting the values in the formula we get EAR = (1 +0.1325/12)^12-1 EAR = 0.14085 EAR = 14.08% 3 Calculation for 18.75% Daily i=0.1875 and n=365 Substituting the values in the formula we get EAR = (1 +0.1875/365)^365 - 1 EAR = 0.206172 EAR = 20.62% 4 Calculation for 14.75% Semi - Annually i=0.1475 and n=2 Substituting the values in the formula we get EAR = (1 +0.1475/2)^2-1 EAR = 0.152939 EAR = 15.29% Number of Times Effective Annual Stated Rate Compounded Interest Rate 12.75% Quarterly 13.37% 13.25% Monthly 14.08% 18.75% Daily 20.62% 14.75% Semi Annually 15.29%