Question

. 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 $200 initially? (Round your answer to the nearest cent.)

Answer 1

SOLUTION:

$f(t)=a(1-\frac{r}{100})^t\text{ }$

Where a = Initial amount ($200), r = rate (7%) and t = time (20 years).

$\begin{gathered} f(20)\text{ = 200 ( 1 - }\frac{7}{100})^{20} \\ f(20)=200(1-0.07)^{20} \\ f(20)\text{ = 200 (}0.93)^{20} \\ f(20)\text{ = 200 (0.2342)} \\ f(20)\text{ = 46.84 ( nearest cents)} \end{gathered}$

CONCLUDSION:

The cost of the item after 20 years will be 46.84 cents.