The Reagan administration got some help this year when it came time to trim the Education Department's budget.

Through the benign intervention of declining interest rates, the department should save a large amount of money in its college student aid programs.

Over the past 15 months, for instance, the department has saved a billion dollars over what it otherwise would have spent "buying down" guaranteed student loans to their subsidized 9 percent rate.

Indeed, along with its fiscal 1984 budget request of $13.2 billion in budget authority, the department has submitted to Congress requests for recissions totaling $1.2 billion in the fiscal 1983 budget, or from appropriations of $15.1 billion down to $13.9 billion, largely to account for lower-than-expected costs in the loan program.

The guaranteed student loan program and a PLUS auxiliary loan program have become the largest federal student aid efforts. Some $6.6 billion worth of loans was made available to 2.8 million students in the current academic year.

For the coming year, the declining interest rates are expected to push the cost of the program down $150 million, but the loan volume is still expected to rise by $600 million and the number of students by 115,000.

Largely because of the high interests rates of 1981 and 1982, higher education's slice of the federal education dollar surpassed the portion received by elementary and secondary education by 48 to 41 percent in fiscal 1982.

But the turnaround in interest rates is expected to close that gap in fiscal 1983 and 1984, with both education levels receiving roughly 44 percent of the total.

In its new budget, the Reagan administration has also proposed a new kind of education savings account, a program to encourage better science and math education and tax credits for parents who send children to private school.

Overall, the nation spent $199.8 billion on education, or 6.8 percent of the gross national product, in the 1981-82 school year. Federal support acounts for 7.7 percent of all spending on elementary and secondary education, and 14.1 percent of all post-secondary education spending.