Final answer:
Mike Gordon needs to invest $74,280 today at an annual interest rate of 2% to have $80,000 in five years. This calculation illustrates the power of compound interest, an essential concept in finance and investments.
Step-by-step explanation:
The question asks about determining the present value that Mike Gordon must invest to achieve his goal of having $80,000 in five years given an annual interest rate of 2%. To calculate this, we use the formula for the present value of a single future amount, which is Present Value (PV) = Future Value / (1 + r)n. Here, r stands for the interest rate and n stands for the number of compounding periods (in years).
So, Mike's calculation would look like this: PV = $80,000 / (1 + 0.02)5. When you do the math, you'll find that the present value he needs to invest today is $74,280.
Understanding the power of compound interest is understated but immensely powerful in growing investments as shown by a theoretical example in the context provided, where $3,000 grows at 7% annual interest rate over 40 years to become $44,923.