Question

If the rate of inflation averages 3.4% per annum over n years, the amount A that $2,500 will purchase after n years is given by the formula A=P(1−0.034)n , where 0.034 is expressed as a decimal. If the inflation rate averages 3.4%, how much will $2,500 purchase in 3 years?

In 3 years, $2,500 will purchase $____ (Round to the nearest cent as needed.)

A. $2,412.65
B. $2,411.55
C. $2,408.10
D. $2,404.82

Answer 1

Using the formula A = P(1 - 0.034)^n, $2,500 will purchase approximately $2,248.39 worth of goods in 3 years with an annual inflation rate of 3.4%, indicating a reduction in purchasing power. The provided options do not match this answer, suggesting an error in the options or the formula application.

Step-by-step explanation:

The question pertains to the impact of inflation on the purchasing power of money over time, and specifically asks how much $2,500 will purchase in 3 years if the annual rate of inflation averages 3.4%. To find the value of $2,500 after 3 years, we use the provided formula A = P(1 - 0.034)n, where P is the initial amount, n is the number of years, and 0.034 represents the inflation rate as a decimal.

Following the given formula, we would calculate it as A = $2,500(1 - 0.034)3. Mathematically, it works out to A = $2,500 × (0.966)3 = $2,500 × 0.899. Calculating these numbers, we get a value close to one of the provided options.

To arrive at the precise amount (rounded to the nearest cent), let's compute the exact values:

A = $2,500 × 0.9663
= $2,500 × 0.899354776
≈ $2,248.39

So, after 3 years, $2,500 will purchase an amount equivalent to $2,248.39. This answer is not listed in the provided options, which indicates there might be a possible error in the question's options or a misinterpretation of the formula's application.