Question

Find the EAR in each of the following cases (Use 365 days a year. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.):

Stated Rate (APR)		Number of Times Compounded	Effective Rate (EAR)
8.0	%	Quarterly		%
17.0		Monthly
13.0		Daily
10.0		Infinite

Answer 1

Ans: EAR= {1 + annual Rate/Number of periods}^ number of Periods -1

1. Stated Rate= 8%

Number of periods= 4

EAR = {1+ 8%/4}^4-1

=> 1+ 2%}*4-1

=> 1+0.02}^4-1=> 1.02^4-1

=> 0.0824 or 8.24%

2. Stated Rate= 17%

Number of Periods= 12

EAR= 1+ 17%/12}^12-1

=> {1+ 0.17/12}^12-1

=> 1+0.0142}^12-1

= (1.0142)^12-1

=> 0.18435 or 18.43%

3. Stated Rate= 13

Number of periods= 365

EAR= 1+ 13%/365)^365-1

=> 1+ 0.0004)^365-1

=> 1.0004)^365-1

=> 0.15716 or 15.71%

4. Stated Rate= 10%

Number of periods= Infinite

EARR = E^RT

=> E^(10%*1)

=> E^ 0.10

=> 2.20