Question

From 1929 through the early 1930s, the prices of consumer goods actually decreased. Economists call this phenomenon deflation. The rate of deflation during this period was about 7% per year, meaning that prices decreased by 7% per year. To get a sense of what this rate would mean in the long run, let's suppose that this rate of deflation persisted over a period of 20 years.

What would be the cost after 20 years of an item that costs $100 initially? (Round your answer to the nearest cent.)
$

Answer 1

Answer:

23.42

Step-by-step explanation:

If something is decreasing by 7% we can mulitply it by (1-.07) or .93

so our formula is

100(.93)²⁰= 23.42388737

which rounds to 23.42

Answer 2

Using the exponential decline function ; the cost of the item after 20 years would be $23.42

Recall :

• $y = A(1 - r)^{t}$
• y = final amount
• A = initial price = $100
• Rate, r = 7% = 0.07
• Time, t = 20years

Substitute the values into the equation :

$y = 100(1 - 0.07)^{20}$

$y = 100(0.93)^{20}$

$y = 100(0.23423887366)$

y = $23.42

Therefore, the cost of the item after 20 years is $23.42

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