Mr. Frohardt donated $40,000 toward future scholarships. The scholarships are to be paid according to the following schedule:
• end of year 1: $1,000,
• end of year 2: $1,500,
• end of year 3: $2,000,
• and so on...
with the amount increasing $500 each year until the scholarship reaches $5,000. The annual scholarship will remain at $5,000 until the fund is depleted. If the account balance is less than $5,000 at the end of any year (i.e., after the awarding of the $5,000 for that year), that remaining amount immediately will be awarded as a smaller scholarship, and the account will be closed. The scholarship fund earns interest at an effective annual rate of 8%. Determine how many full $5,000 scholarships will be awarded.