Consider the following observations of a series:
Year 1 Year 2 Year 3 Year 4
94 114 154 164
a. Calculate the growth rates for Year 1–Year 2, Year 2–Year 3, and Year 3–Year 4. (Round your answers to 4 decimal places.)
b. Calculate the average growth rate. (Enter your answer as a percentage, rounded to 2 decimal places, using intermediate calculations rounded to at least 4 decimal places.)
a.
Growth rate for Year 1 - Year 2:
(114 - 94) / 94 = 0.2128
Growth rate for Year 2 - Year 3:
(154 - 114) / 114 = 0.3509
Growth rate for Year 3 - Year 4:
(164 - 154) / 154 = 0.0649
b.
Average growth rate:
(0.2128 + 0.3509 + 0.0649) / 3 = 0.2095
The average growth rate is 0.2095 or 20.95%.
To calculate the growth rates for Year 1- Year 2, Year 2 - Year 3, and Year 3 - Year 4, we can use the following formula:
Growth rate = (New value - Old value) / Old value
a. Let's calculate the growth rates for the given series:
Year 1 - Year 2:
Growth rate = (114 - 94) / 94 = 0.2128 (rounded to 4 decimal places)
Year 2 - Year 3:
Growth rate = (154 - 114) / 114 = 0.3509 (rounded to 4 decimal places)
Year 3 - Year 4:
Growth rate = (164 - 154) / 154 = 0.0649 (rounded to 4 decimal places)
b. To calculate the average growth rate, we can sum up all the growth rates obtained in part a and divide by the number of growth rates calculated.
Average growth rate = (0.2128 + 0.3509 + 0.0649) / 3 = 0.2095 (rounded to 4 decimal places)
To express this as a percentage, we'll multiply by 100:
Average growth rate = 0.2095 * 100 = 20.95% (rounded to 2 decimal places)
Therefore, the average growth rate for the given series is 20.95%.