# A marketing innovation is the “cash-back mortgage” wherein the lender gives the borrower an…

A marketing innovation is the “cash-back mortgage” wherein the lender gives the borrower an up-front bonus cash payment. For example, if you borrow \$100,000 on a 3% cash-back mortgage loan, the lender will give you \$3000 in addition to the \$100,000 loan. You pay back only the \$100,000 principal over the amortization period. The \$3000 can be immediately applied as a prepayment to reduce the principal balance (to \$97,000) or it can be used for any other purpose. You must keep your mortgage with the lender for at least five years. The cash-back mortgage seems like a good deal, but there is more you need to know about advertised mortgage interest rates. The rates you see posted in your local financial institution are just a starting point for negotiations. You can get _1 4 % knocked off just by asking for it. With some firm negotiating, you can probably get a _1 2 % reduction. If the institution really wants your business, you can get a _3 4 % or even 1% reduction. However, if you take advantage of some other promotion such as a cash-back offer, you will not get any rate discount. So the cash-back offer is not as good as it initially appears.

Which of the following loans should a borrower choose?

• A standard 100,000 mortgage loan at 6.5% compounded semiannually

• A 3% cash-back mortgage loan for 100,000 at 7.25% compounded semiannually

In both cases, the interest rate is for a five-year term and the payments are based on a 25-year amortization. For the cash-back mortgage, assume that the \$3000 cash bonus is immediately applied to reduce the balance to 97,000. (Since the monthly payments are based on the 100,000 face value, the prepayment will shorten the time required to pay off the loan.) Assume money can earn 4.8% compounded monthly.

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