Question

Suppose that you are offered two loans. Loan A has monthly repayments at an APR of 3.9%, and loan B has semi-annual repayments and an APR of 3.95%.

Which loan has a lower effective cost to the borrower? Please show the steps.

Answer 1

Effective cost=[(1+APR/m)^m]-1
where m=compounding periods

A:

Effective cost=[(1+0.039/12)^12]-1

=3.97%(Approx)

B:

Effective cost=[(1+0.0395/2)^2]-1

=3.989%(Approx)

Hence lower effective cost to the borrower is Loan A.