Question

NEED TO CALCULATE EAR

Stated rate (APR)	# of times per year	Effective rate
9.80%	Quarterly
12.40%	Monthly
7.60%	Daily
8.40%	Infinite

Answer 1

Effective annual rate is the interest rate actually earned on the principal due to the effect of compounding.

EAR = ( 1+i/n)ⁿ - 1
where i = interest rate or APR

n = number of compounding period

a) APR = 9.80%
number of time per year n = quarterly or 4 times a year.

EAR = ( 1+ 0.0980/4)⁴ - 1
       = (1+ 0.0245)⁴ - 1
       = 1.101661 - 1
       = 0.101661
       = 10.17%

b) APR = 12.40%
number of time per year n = monthly or 12 times a year.

EAR = ( 1+ 0.1240/12)¹² - 1
       = (1+ 0.010333)¹² - 1
       = 1.131296 - 1
        = 0.131296
        = 13.13%

c) APR = 7.60%
n = 365

EAR = ( 1+ 0.0760/365)³⁶⁵ - 1
       = (1+ 0.00021)³⁶⁵ - 1
       = 1.07895 - 1
        = 0.07895
        = 7.90%

d) APR = 8.40%
n = infinite

EAR = eⁱ - 1
         = 2.71828^0.0840 - 1
          = 1.08763 - 1
          = 0.08763
          = 8.76%