SOLUTION: A recent downturn in economy is causing a man's 401(k) to lose value at a linear rate . On january 1 the account was worth $120,000 and on August 1 it was worth $96,000. If the cur

Question 171447: A recent downturn in economy is causing a man's 401(k) to lose value at a linear rate . On january 1 the account was worth $120,000 and on August 1 it was worth $96,000. If the current trend continues, on december 1 it will be worth how much?
Found 2 solutions by checkley77, nerdybill:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
Using the line equation for this situation we get the 2 points:
(0, 120,000) (8, 96,000)
Y=mX+b where m=slope & b=Y intercept.
First we find the slope:
Slope=(Y2-Y1)/(X2-X1)
Slope=(96,000-120,000)/(8-0)
Slope=(-24,000)/8=-3,000
12000=-3,000*0+b
b=120000 the Y intercept.
y=-3,000x+120,000 is the line equation.
Y=-3,000*11+120,000
Y=-33,000+120,000
y=87,000 is the value of the account on Dec. 1.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A recent downturn in economy is causing a man's 401(k) to lose value at a linear rate . On january 1 the account was worth $120,000 and on August 1 it was worth $96,000. If the current trend continues, on december 1 it will be worth how much?
.
worth along y-axis
months along x-axis
.
january 1 the account was worth $120,000
(1,120000)
August 1 it was worth $96,000
(8,96000)
.
slope
m = (y2-y1)/(x2-x1)
m = (96000-120000)/(8-1)
m = (96000-120000)/(8-1)
m = -24000/7
m = -3428.57 (slope)
.
y = mx + b
96000 = -3428.57(8) + b
96000 = -27428.57 + b
123428.57 = b
.
Our equation of the line is then:
y = -3428.57x + 123428.57
.
where
x is the month (1-12)
y is the worth of portfolio
.
So, to find value for December, set x to 12 and calculate y:
y = -3428.57x + 123428.57
y = -3428.57(12) + 123428.57
y = -41142.84 + 123428.57
y = $82285.73
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