Question 905348: At present, the number of government personnel in NCR is estimated at 450,000. If it gains 2.3% of this number by accession and loses 1.2% of this number by separation regularly each year for 5 years. How many government personnel are there in NCR at the end of the period? ( answer is 474,750 show your solution )
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you start with 450,000
your growth each year is going to be .023 * 450,000 = 10,350
multiply that by 5 and you get a total growth of 5 * 10,350 = 51,750
your losses each year is going to be .012 * 450,000 = 5,400.
multiply that by 5 and you get a total loss of 5 * 5,400 = 27,000.
your net growth is your growth minus your loss which is equal to 51,750 - 27,000 = 24,750.
add 24,750 to 450,000 and you get 474,750.
the formula for the net growth in this problem will be:
f = p + (p * (g - l) * n)
f is the future value
p is the present value
g is the annual growth rate which is the annual growth percent divided by 100
l is the annual loss rate which is the annual loss percent divided by 100
your formula becomes:
f = 450,000 + 450,000 * ((.023 - .012) * 5) which becomes:
f = 450,000 + 450,000 * (.011 * 5) which becomes:
f = 450,000 + 450,000 * .055 which becomes:
f = 450,000 + 24,750 which becomes:
f = 474,750
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