Question

The cost of manufactured goods is rising at the rate of inflation, or at about 3.4%. Suppose an item costs $18 today. How much will it cost seven years from now due to inflation? Round the answer to the hundredth.

Answer 1

To calculate how much an item will cost seven years from now at an annual inflation rate of 3.4%, use the compound interest formula with the present value of $18, giving a future value of approximately $22.78.

Step-by-step explanation:

The question is asking us to calculate the future cost of an item after facing a constant inflation rate over a period of seven years. To determine the future cost, we will use the concept of compound interest, which applies to the inflation rate, just like it does to interest rates in a financial context.

Here's how to do it step-by-step:

1. Identify the present cost of the item, which is $18.
2. Note the annual inflation rate, which is 3.4% or 0.034 in decimal form.
3. Calculate the future value of the item using the formula for compound interest: Future Value = Present Value * (1 + Inflation rate)^number of years
4. Plug in the values: Future Value = $18 * (1 + 0.034)^7
5. Perform the calculation: Future Value = $18 * (1.034)^7
6. Once calculated, we find the future value, which is rounded to the nearest hundredth.

Performing the above calculation, we get:

Future Value = $18 * (1.034)^7 = $18 * 1.265313 = $22.78 (rounded to the nearest hundredth)

Therefore, the cost of the item after seven years, accounting for inflation, would be approximately $22.78.