In a recent stock market downturn, the value of a $5,000 stock is decreasing at 2.3% per month. This situation can be modeled by the equation A(t) = 5,000(0.977)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 ten dollars) after 1 year?

24.4% and $3,780.00
75.6% and $3,780.00
27.6% and $1,380.00
72.4% and $3,620.00

Question

In a recent stock market downturn, the value of a $5,000 stock is decreasing at 2.3% per month. This situation can be modeled by the equation A(t) = 5,000(0.977)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 ten dollars) after 1 year?

 24.4% and $3,780.00
 75.6% and $3,780.00
 27.6% and $1,380.00
 72.4% and $3,620.00

tkhunny · Answer

Have you considered substituting t = 1 into the equation?

anonymous · Answer

No. I really need someone to talk me through this. I am having a really hard time understanding it @tkhunny

tkhunny · Answer

There is no talking through to do.

Problem statement gives: A(t) = 5,000(0.977)^(12t)
Problem statement asks:  after 1 year (or t = 1)
Substitute and calculate.

anonymous · Answer

I got 3,781.85 which would either be A or B if I round. But how would I get the percent? @tkhunny

tkhunny · Answer

Half of 5000 is 2500.  Is 3780 more or less than 2500?

anonymous · Answer

Its more than 2500

tkhunny · Answer

So, the annual rate of discount cannot be as much as 50%, can it?

anonymous · Answer

No, so it would be a?

tkhunny · Answer

There you go.  Think it through.  Reason it out.  Eliminate silly answers.

anonymous · Answer

Ok thanks!