What are points?

Points are fees paid up front to the lender in exchange for a lower interest rate on a mortgage loan. Paying points lowers your mortgage rate because the lender is getting a prepaid portion of the interest rather than collecting it in payments across the term of the loan.

Why We Have the Institution of Points

It is so easy to get into and out of a mortgage in the US that the lenders can't distinguish between those that will keep the loans for a long period of time and those that will keep them for a short period. Those that will keep them for longer periods cost the bank less, in terms of maintenance and selling costs and should receive a lower interest rate.

Points allow the borrower to credibly signal how long they think they will keep the loan. Those that don't take points do so because they are paying a high price now for a short stream of lower payments. Those that intend to keep the loan for a long period of time take points since they anticipate getting the benefits for a longer period of time.

Loan Payments and Balance Remaining with Points

To calculate the payments on the loan, we will use a gross point convention that adds the points into the loan so that the net proceeds from the loan are the same both with and without points. There is also a net points method out in the wild but that will not be covered here.

Payments are simply

\begin{equation} Payment=Principal(1+Points)(A|P,i,n) \end{equation}

For example a \$120,000 30-year mortgage with two points at 6% would have a payment of

\begin{equation} 120,000(1+.02)(A|P,i=(.06/12),360)=733.85 \end{equation}

The balance remaining is as it is for all loans, the present worth of the remaining payments.

Deciding If to Buy Points

Deciding whether or not to buy points on a loan depends on how long you plan to keep the loan. Buying points on a loan will lower your overall interest rate, so if you plan on staying in the home until the amount of money you save due to the lowered interest rate is equal to or greater than the amount you paid for the points(a point costs 1% of the principle). However, if you plan on selling your home soon after you buy it, you will save money if you don't buy points and just put up with higher payments until you sell the house.


From a Previous Midterm
Consider a $120,000 loan, borrowed on 6.75% and two points, what would the monthly payments be?

a) $2,365.46
b) $793.88
c) $801.44
d) $778.32

To calculate first find the monthly payment $120,000 (1.02)(A/P i=(6.75%/12) n=360). This results in a monthly payment of $793.88.

Modified Midterm 2 Points Question

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