Question

if the rate of inflation averages r% per annum over n years, the amount a that $p will purchase after n years is $a = \frac{p}{(1 + r)^n}$, where r is expressed as a decimal. if the inflation rate averages 2%, what will be the purchasing power of $2,000 in 3 years?

in 3 years, $2,000 will purchase $\square$.
(round to the nearest cent as needed.)

Explanation:

Step1: Identify given values

We know \( P = 2000 \), \( r = 2\% = 0.02 \), and \( n = 3 \). The formula for purchasing power is \( A=\frac{P}{(1 + r)^n} \).

Step2: Substitute values into formula

Substitute \( P = 2000 \), \( r = 0.02 \), and \( n = 3 \) into the formula:
\( A=\frac{2000}{(1 + 0.02)^3} \)

Step3: Calculate the denominator

First, calculate \( (1 + 0.02)^3 \).
\( (1.02)^3=1.02\times1.02\times1.02 = 1.061208 \)

Step4: Divide to find A

Now, divide \( 2000 \) by \( 1.061208 \):
\( A=\frac{2000}{1.061208}\approx1884.62 \)

Answer:

\( 1884.62 \)