Question

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.) Stated Rate (AI Effective Rate (EAR) 11.50 % 14.50 % 17.50 % 13.50 % Number of Times Compounded Quarterly Monthly Daily Semiannually

Answer 1

1)

There are 4 quarters in a year

Effective rate = (1 + APR/n)n - 1

Effective rate = (1 + 0.115/4)4 - 1

Effective rate = (1 + 0.02875)4 - 1

Effective rate = 1.120055 - 1

Effective rate = 0.1201 or 12.01%

2)

There are 12 months in a year

Effective rate = (1 + APR/n)n - 1

Effective rate = (1 + 0.145/12)12 - 1

Effective rate = (1 + 0.012083)12 - 1

Effective rate = 1.1550 - 1

Effective rate = 0.1550 or 15.50%

3)

There are 365 days in a year

Effective rate = (1 + APR/n)n - 1

Effective rate = (1 + 0.175/365)365 - 1

Effective rate = (1 + 0.000479)365 - 1

Effective rate = 1.1912 - 1

Effective rate = 0.1912 or 19.12%

3)

There are 2 semi annual periods in a year

Effective rate = (1 + APR/n)n - 1

Effective rate = (1 + 0.135/2)2 - 1

Effective rate = (1 + 0.0675)2 - 1

Effective rate = 1.1396 - 1

Effective rate = 0.1396 or 13.96%

Answer 2

SOLUTION :

Stated rate                 Number of times                   Effective rate

  (APR)                          compounded                            (EAR)

  11.50%                              Quarterly                  (1 + 0.1150/4)^4 - 1 = 0.1201 = 12.01%

 14.50%                             Monthly                  (1 + 0.1450/12)^12 - 1 = 0.1550 = 15.50%

 17.50%                             Daily                  (1 + 0.1750/365)^365 - 1 = 0.1912 = 19.12%

 13.50%                     semiannually                     (1 + 0.1350/2)^2 - 1 = 0.1396 = 13.96%