There are mortgage brokers out there who desperately want to give you a better interest rate, but they can't: Lenders won't let them.

Most lenders don't want brokers selling you too low of an interest rate, so many have imposed discounting restrictions.

That has forced a handful of brokers to become creative in order to offer consumers greater savings. The problem is a handful of brokers have confused creativity with inaccuracy, and their mistakes can cost you.

**Why the discount restrictions?**

Mortgage brokers, like bank reps, can usually sell you a lower rate if they want to. It's called an interest rate "buy-down" and it means the broker has exchanged some of his or her commission for a bigger discount on your mortgage. Most lenders allow this and when they don't, their rate is often uncompetitive.

However, brokers can only go so far. Many banks and credit unions limit broker buy-downs to a set amount like 0.10, 0.15 or 0.25 percentage points off standard rates. They do that to protect their retail franchises from aggressive rate competition and/or to prevent too low a yield when they sell mortgages to investors.

**Where there's a will there's a way**

Lenders may be able to kibosh deep rate discounts but they can't prevent a broker from giving you cash. So some enterprising brokers are now advertising what are called "cashback effective rates."

Cashback effective rates are notional rates that are lower than the lender actually allows. Essentially, the broker figures out the interest cost difference between the lender's actual rate (a.k.a. the "contract rate") and the rate they want to give the customer.

The broker then pays cash to the customer, equivalent to the total interest savings of that lower rate.

Some of today's lowest advertised rates are cashback effective rates. Despite how convoluted this all sounds, this cashback trend is positive for consumers for three reasons:

1) It helps people secure lower overall borrowing costs than they'd otherwise obtain from the lender.

2) It amortizes (pays down) the mortgage quicker since the payment is slightly higher with the higher rate, assuming the borrower uses the cash to prepay the mortgage.

3) The borrower often gets more cash than they're due as most brokers don't apply present value discounts to their cash rebates. In other words, if the higher contract rate means you'll pay $20 more four years from now, most brokers will give you $20 today even though $20 today is worth more than $20 in the future.

**The problem**

A tiny number of brokers seem to have a math impediment. They're essentially overcharging borrowers because they don't calculate the cash rebate correctly. That, by the way, means they're breaking laws that require rate advertising to be clear and not misleading.

For example, I was forwarded an e-mail from one major brokerage that advertises billions in closed mortgages. This company was calculating its cash rebates as simply the difference in payments between the higher rate and the lower rate. That's embarrassingly inaccurate. Among other things, it doesn't take into account the difference in balances when the mortgage term is over.

Another company I saw was calculating the cash rebate as simply the interest cost difference (e.g., 0.10 per cent) multiplied by the mortgage amount. That meant they were only paying the borrower about one year's worth of interest savings even though it was a five-year mortgage!

As York University finance professor Moshe Milevsky duly warns, "Consumers should be vigilant and understand that many of these computations are optical illusions."

**The right way**

According to Prof. Milevsky, the correct way to calculate the rebate on a cashback effective rate is to:

A) Determine the payment difference for each month of the term;

B) Compute the present value of those payment differences each month (using the lower of the two rates as the "discount rate," which is the rate that makes a future sum of money equivalent to an amount today);

C) Total these amounts;

D) Determine the difference in ending balances for each mortgage;

E) Compute the present value of that difference;

F) Add C and E together and give that amount to the borrower.

This is a complex calculation and, believe it or not, few brokers have calculators that can do it. Most brokers simply run two amortization schedules – one for each rate – and then rebate the interest cost difference between the two. This method provides a fair and honest rebate and you can verify that interest cost difference with a mortgage calculator like this one.

**The point here**

Cashback effective rates are the product of a fiercely competitive online mortgage market, where advertising lower rates can be the key to survival for some brokers. Expect more of these rates as time goes on.

If you choose a cashback effective rate, remember to ask your broker how the interest rebate was calculated. Over a lifetime of mortgages, you're bound to uncover math mistakes, and they're not always innocent.

All of this may seem like murky math, but don't let that scare you away from the extra interest savings of cashback effective rates. When calculated and disclosed properly, they are unequivocally beneficial to consumers.

*Robert McLister is a mortgage planner at* intelliMortgage *and founder of* RateSpy.com.