Cost of Finance

Question

Some lenders charge an up-front fee on a loan, which is subtracted from what the borrower receives. This is typically described as “points” (where one point equals 1% of the loan amount). The federal government requires that this be accounted for in the APR that discloses the loan’s cost.

(a) A 30-year mortgage for $220000 has monthly payments at a 6% nominal annual rate. If a borrower’s loan origination fee is 3% (3 points) and it is added to the initial balance, what is the true effective cost of the loan? What would the APR be?

(b) If the house is sold after 6 years and the loan is paid off, what is the effective interest rate and the APR?

(c) Graph the effective interest rate as the time to sell the house and pay off the loan varies from 1 to 15 years?