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Old 04-30-2019, 01:23 PM   #1
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Math Question

Our governor wants to raise the gasoline tax $.20 ($.05 per year for the next 4 years)
The tax is currently 28.6 CPG, if this happens, 4 years later, it would be at 48.6 CPG
‘If’ my math is correct, that's a hike of 69.93%

But when I add the percentages one year at a time, I end up with the following ?

Year 1: 28.6 to 33.6 = 17.48%
Year 2: 33.6 to 38.6 = 14.88%
Year 3: 38.6 to 43.6 = 12.95%
Year 4: 43.6 to 48.6 = 11.47%
56.78%
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Old 04-30-2019, 01:30 PM   #2
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Both numbers are correct. The only problem is not in your math. You’re taking the total increase over the current rate to get the 69.93%. The base assumption you are making is that the twenty cents goes into effect all at one time. But, it doesn’t.

So your table shows the effective increase given that the increase is phased in over 4 years. Which is less than had it been instituted all at one time.
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Old 04-30-2019, 01:38 PM   #3
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The problem is that successive percentages don't add they multiply:

(1 + 0.1748) x (1 + 0.1488) x (1 + 0.1295) x (1 + 0.1147) = 1.70

28.6 x 1.70 = 48.6

So both your individual percentage increases and the total over 4 years result in an overall 70% increase.


Fun Fact: This is also the reason why compound interest yields APRs greater than the sum of daily interest over 365 days.
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Old 04-30-2019, 05:32 PM   #4
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Thanks for the explanations!
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Old 04-30-2019, 05:49 PM   #5
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Originally Posted by ownyourfuture View Post
Thanks for the explanations!

It probably won't happen anyway..... So enjoy the Potholes until another Bridge Falls down.... Then they'll 'Spring into Action'!
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