Question

A scholarship fund pays out 50,000 annually beginning n years from now. To make this go according to plan, annual deposits of 10,000 are made starting today. The credits interest at an annual effective rate of 3% for the first n years and 6.881052981% thereafter. Find n.

Answer 1

The question seeks to calculate the time n required for a scholarship fund to begin annual payments, given annual deposits and varying interest rates. It requires complex financial calculations involving annuities and changing interest rates.

Step-by-step explanation:

The student's question relates to finding the year n when a scholarship fund can start paying out $50,000 annually after making annual deposits of $10,000 starting today. The fund earns an annual effective interest rate of 3% for the first n years and 6.881052981% thereafter.

To solve this problem, we must equate the present value of deposits to the present value of withdrawals, taking into account the two different interest rates for different time periods. We must find n such that the fund has enough to sustain the annual withdrawals of $50,000 indefinitely after n years.

This involves complex time value of money calculations and iterative methods since the interest rate change complicates the usual annuity formulas. Without the explicit formula or steps provided here, the question indicates a need for advanced financial mathematics knowledge, particularly in annuity valuation and time value of money concepts.