We will examine the annual growth rate of the following question.
Formula for calculating the annual growth rate is Growth Percentage Over One year =[ (F÷S) ¹/y - 1] ₓ 100
where F= final value
S= start value
y= Number of years.
(1,350000÷150) y= 2010-1895=115
∴ [(1,350,000÷150) ¹/₁₁₅ - 1] × 100
= (9000¹/₁₁₅ - 1) ₓ 100
= (1.082393 - 1) ₓ 100
= 8.24%
Over the course of 115 years the winners prize money grew from $150.00 to $1,350,000.00, its annual growth rate = 8.24%
Please Note, raising a value a to the ¹/b exponent is equivalent to taking the bth root of a. You will likely need a calculator with an " [tex]\sqrt[n]{x}[/tex]" button, or a good online calculator.
Couldn't find the basic symbols, had to improvise.
The percentage increase per year in the winner's check from 1895 to 2010 is 8.24%
In order to determine the percentage increase per year in the winner's check over the period of 1895 to 2010, the growth rate formula would be used.
[tex]g = (FV / PV)^{\frac{1}{n} } - 1[/tex]
Where:
[tex]($1,350,000 / $150)^{\frac{1}{115} } - 1[/tex] =
[tex](9,000)^{\frac{1}{115} } - 1[/tex] = 0.0824 = 8.24%
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