+476 Robbie, a structural engineer, will earn $64,000 his first year working for a commercial construction company with annual raises of 8%.
What are his total earning at the end of 5 years?
Enter your answer, rounded to two decimal places.
$_____
+36915 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 ! 
)
+36915 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 ! )
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
+36915 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: What you calculated is the FV of an "ordinary annuity" at the END of the period. What I calculated is the also the FV of an "annuity due", or at the BEGINNING of the period!!. In other words, my figure is your figure x 1.08 =$375,462.46 x 1.08 =$405,499.46. By the way, the PV of these 5 payments =$255,533.44.
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.
Here is an example: Regular payment=$1,000. Additional payment=$100. Rate=8%. Period =40 years.
OR: Regular payment =$1,000. Rate=8%. Inflation rate=4%. Period =40 years.
Regular annuity would NOT have an additional $100 or inflation rate of 4%.
+36915 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
