A type of mortgage that is appealing to some borrowers is the cash-back mortgage where the borrower is paid an additional sum on top of the amount of the mortgage. For example, in addition to taking out a $100,000 mortgage, the borrower may get an extra $5000. This amount is marketed as being for closing costs or other house-related expenses, but it is often used to avoid having to save up part or all of the down payment. Trying to figure out if these mortgages are a good deal can be challenging.
We all know that banks aren’t in business to lose money. So they aren’t giving cash back without getting something in return. Typically, they make up the cash back amount by charging a higher interest rate. The borrower might be made to pay the posted mortgage rate rather than a discounted rate. The amount of the cash back depends on the term chosen. The longer you agree to pay an inflated interest rate, the more cash you get back. So, a 5-year fixed term would attract more cash back than a 3-year fixed term.
Suppose that you’re offered a $100,000 mortgage at 5% with a 5-year term, a 25-year amortization, and $5000 cash back. Your monthly payments would be $581.60. How can you tell if this is a good deal? The interest rate is high, but this is offset by the $5000 cash back. More mathematically inclined readers might see that this mortgage is equivalent to a $105,000 mortgage at some lower interest rate with a different amortization period. If we knew the effective interest rate we’d be in a better position to compare this mortgage to other offers.
I created a spreadsheet to calculate the effective interest rate and amortization period for a conventional mortgage equivalent to a cash-back mortgage. The idea is to match the monthly payment, the total amount borrowed, and the outstanding balance at the end of the term. You can save a copy of this spreadsheet in Excel to make changes.
For our example, the spreadsheet calculates that this cash-back mortgage is equivalent to a $105,000 mortgage at 3.82%, a 22.3 year amortization, and no cash back. Using this spreadsheet you can enter your own data on a cash-back mortgage to get an effective interest rate to compare to other mortgage offers.