Question

In a recent stock market downturn, the value of a $500 stock is decreasing at 1.2% per month. This situation can be modeled by the equation A(t) = 500(0.988)12t, where A(t) is the final amount and t is time in years. Assuming the trend continues, what is the equivalent annual devaluation rate of this stock (rounded to the nearest tenth of a percent) and what is it worth (rounded to the nearest whole dollar) after 1 year?

Answer 1

Question 1: What is the annual percentage rate of decrease?
Answer 1: 13.5%

Question 2: What is the stock worth after 1 year?
Answer 2: 433 dollars

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Step-by-step explanation:

I'm assuming the given function is supposed to read A(t) = 500(0.988)^(12t)

If t = 0, then,
A(t) = 500(0.988)^(12t)
A(0) = 500(0.988)^(12*0)
A(0) = 500

If t = 1, then,
A(t) = 500(0.988)^(12t)
A(1) = 500(0.988)^(12*1)
A(1) = 432.566954987969
A(1) = 432.57 <<---- rounding to the nearest penny

Now compute the percent change:
100*(A(1)-A(0))/(A(0)) = 100*(432.57-500)/500 = -13.486
Note: the negative percent change means percent decrease. If the stock were increasing in value, then the percent change would be positive.

The annual percent decrease is roughly 13.486% which further rounds to 13.5%
That takes care of the first part.

To answer the second part, simply round the result for A(1) to the nearest whole number.
So round 432.57 to 433 and that's the answer to the second part.