Question

Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Stated Rate (APR)		Number of Times Compounded			Effective Rate (EAR)
	%		Semiannually		11	%
			Monthly		11.9	%
			Weekly		9.6	%
			Infinite		13.3	%

Answer 1

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

0.11=(1+APR/2)^2-1

(1+0.11)=(1+APR/2)^2

(1.11)^(1/2)=(1+APR/2)

APR=[(1.11)^(1/2)-1]*2

=10.71%(Approx).

2.EAR=(1+APR/m)^m-1
where m=compounding periods

0.119=(1+APR/12)^12-1

(1+0.119)=(1+APR/12)^12

(1.119)^(1/12)=(1+APR/12)

APR=[(1.119)^(1/12)-1]*12

=11.30%(Approx).

3.EAR=(1+APR/m)^m-1
where m=compounding periods

0.096=(1+APR/52)^52-1

(1+0.096)=(1+APR/52)^52

(1.096)^(1/52)=(1+APR/52)

APR=[(1.096)^(1/52)-1]*52

=9.17%(Approx).

4.EAR=(e)^APR-1
where e=2.71828

0.133=(2.71828)^APR-1

1.133=2.71828^APR

Taking log on both sides;

log 1.133=APR*log 2.71828

APR=log 1.133/log 2.71828

=12.49%(Approx).