PV = P(1 - (1 + r)^-n) / r; where P is the periodic withdrawal = $100,000; r = rate = 5% = 0.05; n = number of periods = 20 years.
PV = 100000(1 - (1 + 0.05)^-20) / 0.05 = 100000(1 - 1.05^-20) / 0.05 = 100000(1 - 0.3769) / 0.05 = 100000(0.6231) / 0.05 = 100000(12.4622) = 1,246,221 ≈ $1,250,000
Answer:
see explanation
Step-by-step explanation:
the perimeter (P) is the sum of the 4 sides
(a)
P = a + b + c + d
= x + 7 + 2x + 2 + 8x + x + 10 ← collect like terms
= 12x + 19
(b)
If x = 4 , then
P = 12x + 19 = 12(4) + 19 = 48 + 19 = 67
(c)
If x = 2 , then
P = 12x + 19 = 12(2) + 19 = 24 + 19 = 43
(d)
P = a + b + c + d
= x² + 4x + 8 + 2x² + x ← collect like terms
= 3x² + 5x + 8
The line segment HI has length 3<em>x</em> - 5, and IJ has length <em>x</em> - 1.
We're told that HJ has length 7<em>x</em> - 27.
The segment HJ is made up by connecting the segments HI and IJ, so the length of HJ is equal to the sum of the lengths of HI and IJ.
This means we have
7<em>x</em> - 27 = (3<em>x</em> - 5) + (<em>x</em> - 1)
Solve for <em>x</em> :
7<em>x</em> - 27 = (3<em>x</em> + <em>x</em>) + (-5 - 1)
7<em>x</em> - 27 = 4<em>x</em> - 6
7<em>x</em> - 4<em>x</em> = 27 - 6
3<em>x</em> = 21
<em>x</em> = 21/3
<em>x</em> = 7
7(3r-1)-(r+5)=-52
21r-7-r-5=-52
21r-r-5-7=-52
20r-12=-52
Add 12 to both sides
20r=-40
Divide by 20
r=-2
