Question

In 2016, the automobile industry announced the average vehicle selling price was $35,033. Four years earlier, the average price was $27,880. What was the annual percentage increase in vehicle selling price? (Do not round intermediate calculations and round your final answer to 2 decimal places.) (Omit % sign in your response.)

Answer 1

Given, Initial Price = $ 35,033

Final price = $ 27,880

No.of years = 4 years

Growth can be measured in two ways

1. Calculating Percent (Straight-Line) Growth Rates

Percent Rate = ((Final price - Initial price) / Initial price) *100

= ( ($35,033 - $ 27,880) / $ 27,880 ) * 100 = 25.65%

Therefore, annual growth = Percent rate / no.of years = 25.65% / 4 = 6.41 %

Answer: 6.41% annual growth using Striaght line method.

2. Calculating Average Annual (Compound) Growth Rates

Future price = Initial price * ( 1+ i )^n

where, i = annual growth rate

and n = no. of years

So,

$ 35033 = $ 27,880 * ( 1+i)^4 ==> (1+i)^4 = $ 35,033 / $ 27, 880 = 1.26

==> 1+i = 1.26^(1/4) = 1.059 ==> i = 1.059 - 1 = 0.059

Therefore, i = annual growth rate = 0.059 = 5.9%

Answer: Annual grwoth rate is 5.9% using compound growth rate model