Question

EAR.  What is the effective annual rate​ (EAR) of a mortgage that is advertised at 11.25​% ​(APR) over the next twenty years and paid with semiannual ​payments?

What is the effective annual rate​ (EAR) of the mortgage at 11.25​% APR with semiannual ​payments?

Answer 1

Given the following information,

APR(Annual Percentage Rate) = 11.25% = 0.1125

k = Number of compounding periods per year = semi annual = 2

EAR = Effective Annual Rate = ?

We know that,

1 + EAR = (1 + (APR/k))^k

Rearraging the equation,

EAR = (1 + (APR/k))^k - 1

Substituting the given values in the above equation, we get

EAR = (1 + (0.1125/2))^2 - 1

EAR = (1 + 0.05625)^2 - 1

EAR = (1.05625)^2 - 1

EAR = 1.115664 - 1

EAR = 0.115664 or 11.57%

Thus the effective annual rate​ of the mortgage at 11.25​% APR with semiannual ​payments is 11.57%