Final answer:
To exhaust a $20,000 fund with $1000 payments every six months, 20 payments would be made until the fund is depleted, as the interest earned every six months is equal to the payment amount, thus not affecting the fund balance.
Step-by-step explanation:
The student's question is about calculating the number of $1000 payments that can be made every six months from an education fund of $20,000, considering an interest rate where i² equals 6%, until the fund is exhausted.
To determine the number of payments, one would typically use the formula for either the present value of an annuity or the future value of an annuity, depending on the specific details of the problem. However, this question suggests an account that is depleting, rather than accumulating, which means the present value approach is appropriate.
Given that the interest earned every six months completely offsets the payment, the fund balance would reduce by $1000 every six months without any additional interest accumulation affecting the balance. Essentially, the fund would simply decrease by $1000 every six months until it is depleted.
Therefore, to exhaust a $20,000 fund with $1000 payments every six months, the process would simply involve dividing the total fund by the payment amount:
- Total payments made would be $20,000 / $1000 = 20 payments.
- Since the funds are sufficient to cover exactly 20 payments, no final payment would be needed as the last payment would exhaust the fund.