ElectricPavlov

2.2(14.8r - 3.8) =74,9     Divide both sides of the equation by 2.2

14.8r-3.8 = 34.045          Add 3.8 to both sides

14.8r =37.845                 divide by 14.8

r=2.557

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Yes,  THAT is what we wanted...... the value (present of future) of his total paychecks for 5 years starting at 64000 per year and increasing 8 % per year.     405 K is incorrect.  (you gave him an extra 8%  )

Another point: An increasing/decreasing annuity is an annuity to which either additional payments or an additional percentage(such as the inflation rate) is added to the regular amount or to the regular percentage.

  That is why I set r=0  and g = .08

... 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

225 km / 45 km/hr = 225/45 = 5 hours   + 15 minutes of stop = 5 hr 15 min  

1:10 PM + 5 hr 15 min = 6:25 PM   or   18:25     

 876-720 = 156 degrees

156 x pi/180 = 13/15  pi   

         for a  reference angle    2/15  pi    Radians

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

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 !   )

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

Just add - up the dotted regions.