Question

A lender desires an Effective Yield (EY) of 4.00% with an expected average loan payoff in 7 years. A borrower wants a $400,000 loan for 30 years at 3.20%, compounded monthly. Without a prepayment penalty, how many discount points must the lender charge to achieve an EY of 4%?

a) 0
b) 1
c) 2
d) 3

Answer 1

To achieve an Effective Yield of 4% on a $400,000 loan for 30 years at 3.20% compounded monthly, the lender must charge 3 discount points.

Step-by-step explanation:

To achieve an Effective Yield (EY) of 4% on a loan, the lender must charge discount points. Discount points are upfront fees paid by borrowers to lenders to lower the interest rate on the loan. Each discount point is equal to 1% of the loan amount. To calculate the number of discount points needed, we can use the present value formula and the loan's cash flows.

In this case, the borrower wants a $400,000 loan for 30 years at 3.20% compounded monthly. Let's assume the lender charges x discount points. The present value of the loan's cash flows would be:

Present Value = $400,000 - (x * 0.01 * $400,000)

To achieve an Effective Yield of 4%, the lender wants the Present Value to be equal to:

Present Value = $400,000 * (1+0.04)¯' 30

By equating the two Present Value formulas and solving for x, we can determine the number of discount points:

x = 3