When the Corporation voted last week to raise the cost of attending the College by nearly 15 percent, students and parents who will face staggering bills in excess of $12,000 wondered why.

With the University's endowment at $1.6 billion and with inflation below 10 percent, why should student charges increase at double-digit rates for the third straight year?

The answer often given by University administrators is that declining federal support and the failure of the endowment to keep pace with inflation place the burden of making up the difference disproportionately on students.

Most people can understand the problem of declining government assistance. But to those unfamiliar with Harvard's labyrinthine financial structure it is difficult to comprehend why an institution with more than a billion dollars invested in stocks and bonds can't rely more on income from those investments to offset costs.

The answer, according to Robert H. Scott, director of financial systems, is twofold. A number of expenses, he says, are increasing much faster than inflation. The most notable such cost to the University is student aid.

And, more significantly, the endowment income distributed for use by the University's many faculties and departments has not kept pace with inflation, Scott says.

Income from endowment, which amounted to $131.1 million in 1980-81, is one of several sources of revenue, including government funds, private donations and student fees, for Harvard's ten faculties. Endowment income generally increases as the value of the endowment rises.

The total value of the endowment can increase in several ways: through gifts; through increases in the value of stocks and bounds in Harvard's portfolio, and through the reinvestment of interest and dividends earned on investments.

During the 1970s, Harvard's endowment grew at a rate that failed to keep pace with inflation and Harvard's financial managers, who maintain a long-term perspective regarding the endowment, had to rely on reinvesting income to keep the endowment from losing too much ground. Because the University relies on endowment income both to bolster endowment value and to help support faculties and departments, administrators must determine a "prudent" balance between those purposes.

Harvard's 1980-81 financial report shows where the University stands regarding that balance, stating that "the value of the endowment can be maintained only through a conservative distribution policy that retains a fraction of current income to build the capital base. Failure to follow such a policy would assist current operations, but only at the expense of the University's ability to maintain those same endowment-dependent activities in the future."

Or, as Thomas O'Brien, the University's financial vice president, puts it..."You can't increase the endowment income distribution rate as rapidly as inflation because you'd eat out your entrails," Eroding the endowment might alleviate current financial woes, but it would hurt future generations of Harvard students, financial officials say.

Despite the persistence of economic difficulty during the last decade, Scott and O'Brien seem hopeful that as inflation slows, so will tuition increases. More specifically, Scott says "tuition won't rise as rapidly, only when endowment values increase at a rate equal to inflation." That will happen, he continues, only with a general improvement in the economy and the financial markets.