Question

Instead of investing a lump sum of $25,000, Brittany Royer decides to save the money in a vault for 2 years. Assuming the inflation being 2.5% per year, how much will her purchasing power decline in 2 years time?

a. $1,562.50
b. $1,280.25
c. $1,616.25
d. $1,345.00

Answer 1

The decline in Brittany Royer's purchasing power in 2 years due to an annual inflation rate of 2.5% is calculated using the future value formula considering inflation, resulting in a value slightly higher than the provided options.

Step-by-step explanation:

The question deals with the concept of inflation and its effect on the purchasing power of money over time. To calculate how much Brittany Royer's purchasing power will decline in 2 years with an annual inflation rate of 2.5%, we need to apply the formula for calculating the future value in terms of present value taking into account inflation.

Using the formula (1 + inflation rate)^number of years, the rate at which prices increase over the two years can be found as follows:

(1 + 0.025)^2 = 1.050625

We multiply this rate by the initial amount of $25,000 to get the future cost equivalent of the current sum:

$25,000 * 1.050625 = $26,265.625

Now we subtract the original amount from this to find the decline in purchasing power:

$26,265.625 - $25,000 = $1,265.625

The closest answer, which is likely due to rounding in the options, would be (d) $1,280.25. This is not an exact match to our calculation, so it is likely that the decline in purchasing power will actually be slightly less than one of the provided answers due to rounding.