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.

18 full scholarships will be awarded

Explanation:

year       beginning     interest     scholarship    ending

               balance        earned  awarded       balance

1        40000        43200        1000        42200

2        42200        45576        1500        44076

3        44076        47602        200045602

4        45602        49250        250046750

5        46750        50490        300047490

6        47490        51289        350047789

7        47789        51613        400047613

8        47613        51422        450046922

9        46922        50675        500045675

10           45675        49329        500044329

11        44329        47876        500042876

12           42876        46306        500041306

13        41306        44610        500039610

14           39610        42779        500037779

15           37779        40801        500035801

16        35801        38666        500033666

17        33666        36359        500031359

18        31359        33868        500028868

19           28868        31177        500026177

20        26177        28271        500023271

21        23271        25133        500020133

22        20133        21743        500016743

23        16743        18083        500013083

24        13083        14129        50009129

25        9129                 9860        50004860

26        4860        5249        5000249

you will have $2593.74 in 10 years if you set aside $1,000 at 10%

you will have $9321.91 in 20 years if you set aside $2000 at 8%

you will have $1469.32 in 5 years if you set aside $1000 at 8%

you will have $1296.87 in 10 years if you set aside $500 at 10%

you will have $239.66 in 15 years if you set aside $100 at 6%

you will have $4660.96 in 20 years if you set aside $1000 at 8%