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A company has revenues of $100 during Year 1. Each year their profit is 20% of revenue. Revenue is growing 15% per year. How much total profit (rounded to the nearest penny) will the company earn during Years 1-10

Respuesta :

Answer:

$406.07

Explanation:

Revenue for year 1 = $100

Profit = 20%

Growth rate of revenue, = 15% per year = 0.15

Now,

year 1 is the base year thus, take it as n = 0

Revenue for the year = $100 × ( 1 + r )ⁿ

Profit = 20% of [$100 × ( 1 + r )ⁿ]

Year       n              Revenue               Profit

  1           0            $100( 1 + r )⁰            $20

  2          1            $100( 1 + r )¹             $23

  3          2            $100( 1 + r )²            $26.45

  4          3            $100( 1 + r )³            $30.4175

  5          4            $100( 1 + r )⁴            $34.98

  6          5            $100( 1 + r )⁵            $40.227

  7          6            $100( 1 + r )⁶            $46.261

  8          7            $100( 1 + r )⁷            $53.2004

  9          8            $100( 1 + r )⁸            $61.1804

  10         9            $100( 1 + r )⁹            $70.357

   Hence,

Total profit for the year 1 - 10 = $406.07

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