Question

Suppose that prices increase 2.5% each year for 10 years. How much will a jacket that costs $100 today cost in 10 years? Hint: Think of the cost as the balance in a savings account with an APY of 2.5% and an initial investment of $100. (Enter your answer to the nearest dollar and do not include a dollar sign or decimal points in your answer.)

Answer 1

Explanation:

If the price of the jacket increases 2.5% each year for 10 years, we can think of the price increase as the interest earned on an initial investment of $100 with an annual percentage yield (APY) of 2.5%. We can use the formula for compound interest to calculate the future value of the investment after 10 years:

FV = PV x (1 + r)^n

where FV is the future value, PV is the present value (initial investment), r is the annual interest rate (as a decimal), and n is the number of compounding periods (years).

In this case, PV = $100, r = 0.025 (2.5% expressed as a decimal), and n = 10. Plugging these values into the formula, we get:

FV = $100 x (1 + 0.025)^10

FV ≈ $128

Therefore, the jacket that costs $100 today will cost approximately $128 in 10 years if the price increases 2.5% each year.