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.): 

Answer 1

Stated Rate	Number of times compounding
8.90%	quarterly
EAR = (1+i/n)^n - 1
where i is the stated rate that is 8.90%.
and n is the number of compounding periods that is 4.
EAR = (1+.0890/4)^4 - 1
EAR = (1+.02225)^4 - 1
EAR = 1.092015 - 1
EAR = .092015
The EAR is 9.20%.
Stated Rate	Number of times compounding
17.90%	monthly
EAR = (1+i/n)^n - 1
where i is the stated rate that is 17.90%.
and n is the number of compounding periods that is 12.
EAR = (1+.1790/12)^12 - 1
EAR = (1+.014917)^12 - 1
EAR = 1.194441 - 1
EAR = .194441
The EAR is 19.44%.
Stated Rate	Number of times compounding
13.90%	daily
EAR = (1+i/n)^n - 1
where i is the stated rate that is 13.90%.
and n is the number of compounding periods that is 365.
EAR = (1+.1390/365)^365 - 1
EAR = (1+.000381)^365 - 1
EAR = 1.149094 - 1
EAR = .149094
The EAR is 14.91%.
Stated Rate	Number of times compounding
10.90%	infinite
EAR = (e^(.109))-1
e = 2.71828
EAR = (2.71828^(.109))-1
EAR = 1.115162 - 1
EAR = .115162
The EAR is 11.52%.
Stated Rate	Number of times compounding	EAR
8.90%	quarterly	9.20%
17.90%	monthly	19.44%
13.90%	daily	14.91%
10.90%	infinite	11.52%

Answer 2

SOLUTION :

Stated rate                 Number of times                   Effective rate

  (APR)                          compounded                            (EAR)

  8.9%                              Quarterly                  (1 + 0.089/4)^4 - 1 = 0.092   =   9.20%

 17.9%                             Monthly                 (1 + 0.179/12)^12 - 1 = 0.1944 = 19.44%

 13.9%                             Daily                   (1 + 0.139/365)^365 - 1 = 0.1491 = 14.91%

 10.9%                             Infinite                             e^(0.109*1) - 1 = 0.1152 = 11.52%