Question

The officers and board of directors of the institute of Integrated Electrical Engineers desire to award a Php 3,600 scholarship annually to deserving electrical engineering students for as long as its scholarship fund shall last. The fund was started July 1, 1987 by a donor in the amount of Php 18,000. The IIEE invested this amount at that time at 8% per annum and plans on adding Php 600 each year to the fund from its dues starting July 1, 1988 for as long as awards are made.

a.For how many years starting July 1, 1988 can scholarship be awarded?

b.What will be the balance in the fund after the last award is made?

Answer 1

(18000(1.08)+600-3600)(1.08)+600-3600)(1.08)+600-3600)(1.08).....=0

(18000(1.08)-3000)(1.08)-3000)(1.08)-3000)(1.08).....

18000(1.08)^n-3000)(1.08)^(n-1)-3000(1.08)^(n-2)....=0

This is the construction of payment and income which ends ay year y where all the fund gets down to less than 3600 php

Using excel to identify y

We found that at End of year 7 the total fund first time will go below 3600 php

Hence for 7 years scholarship will be awarded

Answer for B)

Balance left is  1406.87 php

End of year	18000(1.08)^(End of Year)-3000
1	16440
2	14755.2
3	12935.616
4	10970.46528
5	8848.102502
6	6555.950703
7	4080.426759
8	1406.8609