HIGH INTEREST RATES are now making several kinds of trouble for the Reagan administration. It's possible to argue that the prime rate, in its latest jump, is only following recent rises in other rates. But it means, at the least, that the banks don't expect the pattern to change immediately. For the president, it's more than an irritation.

As the world's biggest borrower, the federal government is paying interest at a pace that is now creeping toward $100 billion a year -- 15 cents out of every dollar in the budget. The administration's economic planning assumed that the interest rate, for example, on three-month Treasury bills would average a little over 11 percent for the fiscal year ending in September. So far, the rate has averaged about 14 percent, and one day last week, culminating the past month's rise, it hit 17 percent.

Much more important than this direct cost, the rise in interest rates this spring reflects the financial markets' lack of faith in the Reagan administration's economic theory. It is essential to the administration that the financial people accept and support its logic, because the plan's success depends on a rapid and vigorous response from the lenders and the investors. But the interest rates indicate that they remain dubious, and are even backing off a little.

Then, if the high rates persist, there will be the further effects on industry -- starting with automobiles and home building, but eventually reaching, to one degree or another, just about every kind of business. The administration is urgently anxious to help the automobile manufacturers in particular. But it has little room for maneuver.

Traditionally, the way for a president to lower interest rates has been to persuade the Federal Reserve to increase the money supply faster. But the Reagan administration has repeatedly pledged tight restraint on the money supply and, in any case, it hasn't much choice. This country's experience with high inflation is foreclosing many of the traditional devices that presidents have used in the past. If the Federal Reserve were to reverse course and begin pumping out money faster, the result in the present atmosphere would be anything but lower interest rates. On the contrary, people would immediately suspect another capitulation to inflation and, as the lenders struggled to protect themselves from the consequences, interest would go higher than ever. That's why both the administration and the Federal Reserve have been adamant about the need to keep the money supply under tight control.

The central error in the administration's theory is its belief that it can have everything it wants simultaneously -- accelerating economic growth, falling inflation, tight money and declining interest rates. So far it has maintained tight money, and inflation has begun to show preliminary signs of slowing down. But higher growth with lower interest rates will require the kind of changed in people's outlooks that cannot occur quickly. It will take time to persuade the country that the changes in public policy and economic performances are real and reliable. Inflation will have to come down convincingly, and remain down for more than a few months, before low and stable interest rates again become possible.