Question

Find the APR, or stated rate, 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.):

Stated Rate (APR)	# of times Compounded	Efective rate (EAR)
	semiannual	11.3%
	monthly	12.2%
	weekly	9.9%
	infinite	13.6%

Answer 1

a.EAR=[(1+APR/m)^m]-1
where m=compounding periods

0.113=(1+APR/2)^2-1

(1+0.113)=(1+APR/2)^2

APR=[(1+0.113)^(1/2)-1]*2

=11%(Approx).

b.EAR=[(1+APR/m)^m]-1
where m=compounding periods

0.122=(1+APR/12)^12-1

(1+0.122)=(1+APR/12)^12

APR=[(1+0.122)^(1/12)-1]*12

=11.57%(Approx).

c.EAR=[(1+APR/m)^m]-1

where m=compounding periods

0.099=(1+APR/52)^52-1

(1+0.099)=(1+APR/52)^52

APR=[(1+0.099)^(1/52)-1]*52

=9.45%(Approx).

d.

EAR=(e)^APR-1

where e=2.71828

0.136=(2.71828)^APR-1

1.136=2.71828^APR

Taking log on both sides;

log 1.136=APR*log 2.71828

APR=log 1.136/log 2.71828

=12.75%(Approx).