SOARING INTEREST RATES present the Reagan adminstration with an interesting dilemma. The last great surge in these rates, last March and April, chiefly hit housing and automobile sales. Unemployment rose, concentrated in those two industries. Over the summer, Mr. Reagan made much of the "Carter recession" and declared that a rightminded economic policy could get everyone promptly back to work. As you have probably noticed, he won the election. Now interest is moving upward again, and again it is the housing and automobile industries, with their extreme dependence on mortgage and bank loan rates, that are chiefly threatened.

The rates are going up because the Federal Reserve Board is trying to limit bank lending, while a lot of corporations are anxiously trying to borrow. The Federal Reserve's purpose is, of course, to try to hold down inflation. As for the corporations, some of them would normally have chosen to raise money by selling bonds. But the interest cost of bonds has been rising steadily since last spring, and, while they wait for better times, these big borrowers have gone to the banks for shorter-term loans. This week the banks' prime rate was bid up to 16 1/2 percent.

Perhaps a new administration might think of leaning on the Federal Reserve to relax and let the rates come down a little. If you were a lender on a large scale, you would then react by seeing what rates were available abroad. If you were that kind of a lender, you would be looking worldwide for the best real rate of return -- which means interest adjusted for inflation. You would note that the prime rate in Germany is less than 12 percent. But since the inflation in Germany next year is likely to be only 4 percent, compared with 10 percent in this country, you might reasonably conclude that the real return was better in Frankfurt -- and exchange your dollars into Deutschemarks.

As American interest rates dropped, a lot of people would do precisely that, and the value of the dollar would begin to slide downward. That's a currency crisis, and it's intolerably dangerous. But if interest rates remain high, it will get harder than ever to sell cars and houses. There's the dilemma.

The United States is now the center of an international financial system that pays increasingly little attention to national boundaries. That system has made large contributions to American prosperity, but the price is the loss of a degree of independence in setting domestic economic policy. Perhaps, in fact, there is no longer any real distinction between domestic and foreign economic policy. It's certainly true that if a president genuinely tries to hold the line against inflation, he can have very little influence over interest rates that are now set by world markets. A good many people in Washington have made that discovery over the last several years. But it's never easy to explain in Detroit or, for that matter, on Main Street.