Question

A lender wants an EY of 4.00% and expects an average loan payoff in 7 years. However, a particular borrower wants to borrow $400,000 for 30 years at 3.20%, compounded monthly.

First, without charging a prepayment penalty, how many discount points must the lender charge to have an EY of 4%?
a) 0.5 points
b) 1 point
c) 1.5 points
d) 2 points

Answer 1

To have an EY of 4%, the lender must charge approximately 0.5 points in discount points.

Step-by-step explanation:

To determine the number of discount points the lender must charge without a prepayment penalty in order to have an effective yield (EY) of 4%, we need to compare the cost of the loan to the desired yield. First, let's calculate the cost of the loan without discount points. The borrower wants to borrow $400,000 for 30 years at 3.20% compounded monthly. We can use the present value (PV) formula to calculate the total cost of the loan:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where PV is the present value (total cost of the loan), C is the constant monthly payment, r is the monthly interest rate, and n is the total number of months. Plugging in the values, we get:

PV = 400,000 * [(1 - (1 + 0.032/12)^(-30*12)) / (0.032/12)]

PV ≈ $573,847.99

Now, let's calculate the cost of the loan with discount points to achieve an EY of 4%. We will use the following formula:

Discount Points = PV * (1 - (1 + EY)^(1/n))

Where Discount Points is the amount of discount points the lender must charge, PV is the present value (total cost of the loan), EY is the desired effective yield, and n is the total number of years. Plugging in the values, we get:

Discount Points = 573,847.99 * (1 - (1 + 0.04)^(1/30))

Discount Points ≈ 0.5 points

Therefore, the lender must charge approximately 0.5 points in discount points.