Final answer:
To determine the future value after y years for an invested amount, the compound interest formula FV = Principal × (1 + interest rate)^time is used. Using a 7% real annual rate of return, a $3,000 investment would grow to $44,923 over 40 years.
Step-by-step explanation:
Understanding Compound Interest for Future Value Calculations
To calculate how much money you would have after y years when you invest a certain amount, often referred to as the future value account (FVA), the formula for compound interest is used. This is especially relevant when making choices about savings and investment early in life, harnessing the power of compound interest over long periods. Let's say at age 25, someone saves and invests $3,000 in a diversified stock portfolio assuming a 7% real annual rate of return. This rate is actually 7% above inflation.Using the compound interest formula, which is Future Value (FV) = Principal × (1 + interest rate)time, where Principal is the initial amount invested, interest rate is the rate at which the investment grows per period, and time is the number of periods (years in this case), we can forecast the investment growth over y years. For example, for a period of 40 years: $3,000 × (1 + 0.07)40 = $44,923.
Applying this to different scenarios like receiving future payments from a firm or calculating GDP growth over a set number of years fundamentally relies on the same mathematical principle. It's important to note that compound interest results in exponential growth due to interest being calculated on the accumulated interest from the previous periods as well as the principal amount.