NEW YORK ( MainStreet — Now that the Federal Reserve has finally announced the start of its "taper," should mortgage shoppers get a move on to beat higher rates?

They probably should, but not because mortgage rates will spike. Instead, borrowers might want to beat fee increases this coming spring from Fannie Mae and Freddie Mac , the two firms that back most new mortgages. The hike could add thousands of dollars to your closing costs.

The smart money says mortgage rates will probably drift up, but slowly; the Fed's decision to cut back on its bond-buying program has been expected for some time and is baked into current mortgage prices.

In fact, the financial markets were thrilled last week when the Federal Open Market Committee said the taper would take all of next year to reduce the monthly bond purchases, now at $85 billion a month, to zero. Those purchases have been designed to keep long-term interest rates low.

The FOMC also signaled that it probably would not start raising short-term rates for two years. So not many experts foresee a spike in loan rates.

But Fannie and Freddie, the government-owned companies, are raising a key fee to offset risks and help a government effort to rekindle the market for loans that are not backed by these two firms. As a result, closing costs will rise as lenders work the new fees into loan prices, perhaps as soon as March.

The fee, called a "risk based premium" or "loan level pricing adjustment" will be large enough to more than offset the elimination of another fee, the Adverse Market Delivery Charge of 0.25% of the loan amount. The new fees will be higher for borrowers with low credit scores or who make low down payments.

An example prepared by HSH.com, the mortgage information service, shows the effect on a borrower with a good credit score of 740 who puts 20% down. Currently, that borrower would be charged $250 each in AMDC and LLPA for every $100,000 borrowed, for a total of $500.

With the changes, the AMDC fee will disappear but be replaced by a 1.5% LLPA, for a total of $1,500 per $100,000. That could raise the losing costs on a $300,000 loan by $3,000.

While borrowers with higher credit scores will pay slightly less, the size of the down payment is a bigger factor in setting the fee level. That's because a lower ratio between the loan amount and the home's value reduces the lender's risk of loss in a foreclosure .

A borrower with a 740 credit score would pay a 1.5% fee with a down payment of 15% or less, but only 0.75% with a 20% down payment. If that buyer could increase his or her credit score to 779, the fee would still be 0.75%. with 20% down.