Final answer:
The student's question about calculating the future value of an annuity investment of $6000 annually at an 8% return over 20 years involves using the formula for the future value of an annuity compounded annually and highlights the power of compound interest.
Step-by-step explanation:
Calculating the Future Value of an Annuity
The question involves the concept of the Time Value of Money, specifically calculating the future value of an annuity. An annuity is a series of equal payments made at regular intervals over a period. In this scenario, an individual invests $6000 annually over a 20-year period at an 8% return. To determine the future value of this annuity, we use the formula for the future value of an annuity compounded annually:
FV = P × {[(1 + r)^n - 1] × [1/r]}
where:
- FV is the future value of the annuity.
- P is the annual payment ($6000).
- r is the annual return rate (0.08).
- n is the number of years the money is invested (20).
Using these values:
FV = 6000 × {[(1 + 0.08)^20 - 1] × [1/0.08]}
A calculator can be used to compute the actual future value, which will demonstrate the power of compound interest over time. Starting to save early and consistently can result in substantial growth due to compounding, as illustrated by earlier examples where a one-time investment can grow many-folds over a lengthy period.