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# Math

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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.

\$_____

Dec 19, 2018

#1
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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 ! )

Dec 19, 2018

#1
+2

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 ! )

ElectricPavlov Dec 19, 2018
#2
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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

Dec 19, 2018
edited by Guest  Dec 19, 2018
#3
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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

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

ElectricPavlov  Dec 19, 2018
edited by ElectricPavlov  Dec 19, 2018
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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%.

Dec 19, 2018
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deleted

ElectricPavlov  Dec 20, 2018
edited by ElectricPavlov  Dec 20, 2018
#5
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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

Dec 20, 2018
edited by ElectricPavlov  Dec 20, 2018