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How is the Present Value of a Growing Annuity Derived?

The present value of a growing annuity is the sum of future cash flows. For a growing annuity, each cash flow increases at a certain rate.

...or it is equal to

64000 + 64000(1.08) + 64000(1.08)^2 + 64000(1.08)^3 + 64000(1.08)^4

64000 (1 + 1.08 + 1.08^2 + 1.08^3 + 1.08^4) = $ 375462.46

More info here:

http://financeformulas.net/Present_Value_of_Growing_Annuity.html

Here is a FUTURE VALUE calculation if you prefer: (to avoid confusion)

FV = P [(1+r)^n - (1+g)^n]/(r-g)           same answer......

http://financeformulas.net/Future-Value-of-Growing-Annuity.html

EP: Why did you calculate the PV instead of FV? Isn't it what the questioner is asking for?
s=listfor(n, 1, 5, (64000*1.08^n);prints, "FV =",sum(s)
($69,120.00, $74,649.60, $80,621.57, $87,071.29, $94,037.00) FV = $405,499.46

Thankyou!!

Triangle DBC is  a 3-4-5  right triangle

So  BC = 5

And AB = 20 - 5   =  15

So....since BDis parallel to AE.......we have this relationship

BC/ AB = CD/DE

5/15 = 4/DE

15/5 = DE /4

3 = DE/4   multiply both sides by 4

12 = DE

So 

EC = ED + DC  =  12 + 4  = 16

And by the Pythagorean Theorem,

AE = sqrt [ AC^2 - EC^2 ]  =  sqrt [ 20^2 - 16^2 ] =  sqrt [ 400 - 144] = sqrt [ 256] =  16 ft

The conditional probability of Event B given Event A is P(B|A)=P(A and B)/P(A) when two events are not independent.

I got 433 as well.

I think the confusion stems from whether a digit can be repeated or not. 

CPhil looks to be assuming they cannot.

There's nothing in the problem that states they can't.

The full list of numbers is

{200, 202, 201, 209, 220, 222, 221, 229, 210, 212, 211, 219, 290, 
292, 291, 299, 100, 102, 101, 109, 120, 122, 121, 129, 110, 112, 111, 
119, 190, 192, 191, 199, 900, 902, 901, 909, 920, 922, 921, 929, 910, 
912, 911, 919, 990, 992, 991, 999}

and this has mean 433

this curve produces the following points

(0,1), (2, 4)

the average rate of change between these two points is just the slope of the line connecting them.

\(m = \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{4-1}{2-0} = \dfrac 3 2\)

​f(x)​ is greater than ​g(x)​ on the interval ​ (0,1) ​.

​f(1) is equal to g(1) .

–3p and 13p

Rate of change from [9,10 ] = [11014 - 4052] / [10 - 9]   = 6962

Rate of change on  [ 5, 8] = [ 1491 - 75] / [ 8 - 5]  = 472

So

6962 / 472  =    14.75 times as great

P.S.  -  not sure if this is the answer that is wanted...

Second one

MA =  46.2 - 14  =   32.2

BP =  72.6 - x

So, again, we have this relationship

MA /  NA  = MB / BP

32.2/ 14  = x /  [ 72.6 - x ]      cross-multiply

32.2 [ 72.6 - x ]   = 14x     simplify

2337.72 - 32.2x  =  14x        add 32.2x to both sides

2337.72 =  46.2x      divide both sides by 46.2

50.6   =  x

( -5 + i ) * i         -5i + i^2           -5i - 1          - (5i + 1)        5i + 1

_________ =    _______  =   ________ =  _______   =   _______

   2i * i                  2i^2               -2                   -2                    2

First one :

Since we have a segment parallel to a base of a triangle,the sides are in equal proportion...so....

121/ 11 =  (5x + 10)  / 10

11 =  (5x + 10) / 10      multiply both sides by 10

110  = 5x + 10      subtract 10 from both sides

100 = 5x    divide both sides by 5

20  =  x

The first is true

The y intercept of g(x)  = -4

The y intercept of f(x) = 2

The second is false

f(x) is positive on this interval

g(x) is negative on this interval

The third is true

Max of g(x)   = 5

Max of f(x) = 2

The last is true

The x intercepts for both are  x =-2  and x = 2

CORRECT  !!!

The mean is 49.1

The standard deviation is  27.8

So.....one SD from the mean is  from

49.1 - 27.8       to    49.1 + 27.8   =

21.3     to    76.9

6 scores fall into the range = 6/10 =  60%

This is lower than expected   (we expect 68% to fall witin the range )

yeppers.

PV =  p /(r-g) [ 1 - {(1+g)/(1+r)}^n}]       r = 0   g = .08   n = 5   P = 64000

PV = 64000/(-.08)   *  ( -.469328)

= $ 375462.46                  (minus a  HUGE chunk for TAXES !   )

C(10, 5) *  (1/2)^5 * (1/2)^5   =  .246  = 24/6%

Number 6?

3 ^{x^2 - 42}   =   1 / 3^x

Note that the term on the right side can be written as 3^-x

So   we have

3 ^{x^2 - 42}  = 3 ^-x

Since the bases are the same, we can solve for the exponents

x^2 - 42 = - x       add x to both sides

x^2 + x - 42 = 0       factor

( x + 7) ( x - 6) =  0

Setting each factor to 0 and solving for x produces  the integer solutions

x = -7    or    x = 6

P(A l B  )   = P (A and B) / P(B) =     0.2 / 0.4  =   0.5

Independent because    P(A l B) = P(A)

(f-g)(x) = f(x) - g(x) =   x^4 - x^3 -2x^2 - 4x +12

99.7% of the data  fall within 3 standard deviations from the mean

So....

Low end of the range is  60 - 3(4.5)  = 46.5 in

High end of the range s 60 + 3(4.5)  = 73.5 in