Question

Consider an investment in a security with a face value of EUR 1,000 that makes interest payments at a nominal annual rate of 12%. Find the equivalent annual effective rate, under the following assumptions:

1. a) interest is paid once at the end of the year (m = 1);

2. b) interest is paid at the end of every semester, i.e. twice in a year (m = 2);

3. c) interest is paid at the end of every month, i.e. twelve times in a year (m = 12).

Answer 1

Question a:

r = Nominal Interest rate = 12%

m = 1

Equivalent annual effective rate = [1+(r/m)]^m - 1

= [1+ (12%/1)] ^1 - 1

= 1.12 - 1

= 12%

Equivalen Annual Rate is 12%

Question b:

r = Nominal Interest rate = 12%

m = 2

Equivalent annual effective rate = [1+(r/m)]^m - 1

= [1+ (12%/2)] ^2 - 1

= 1.1236 - 1

= 12.36%

Equivalen Annual Rate is 12.36%

Question c:

r = Nominal Interest rate = 12%

m = 12

Equivalent annual effective rate = [1+(r/m)]^m - 1

= [1+ (12%/12)] ^1 - 1

= 1.12682503 - 1

= 12.68%

Equivalen Annual Rate is 12.68%