Question

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

Stated Rate (APR)	Number of Times Compunded	Effective Rate (EAR)
8.4%	Quarterly
17.4	Monthly
13.4	Daily
10.4	Infinite

Answer 1

a.

APR of 8.40% compounded quarterly, so effective annual rate is calculated below:

Number of quarter in a year = 4

Effective annual rate = [(1 + 8.40% / 4) ^ 4] - 1

= 1.0867 - 1

= 8.67%

Effective annual rate is 8.67%.

b.

APR of 17.40% compounded monthly, so effective annual rate is calculated below:

Number of month in a year = 12

Effective annual rate = [(1 + 17.40% / 12) ^ 12] - 1

= 1.1886 - 1

= 18.86%

Effective annual rate is 18.86%.

c.

APR of 13.40% compounded daily, so effective annual rate is calculated below:

Number of days in a year = 365

Effective annual rate = [(1 + 13.40% / 365) ^ 365] - 1

= 1.1434- 1

= 14.34%

Effective annual rate is 14.34%.

d.

APR of 10.40% compounded infinite, so effective annual rate is calculated below:

Effective annual rate = [e ^ (r × t)]- 1

= [2.718 ^ (10.40% × 1)] - 1

= 1.1096 - 1

= 10.96%

Effective annual rate is 10.96%.