Final answer:
To retire with an annual income of $50,000 for 30 years at a 5% return, you must calculate the present value of an annuity. Using the formula PV = PMT × [(1 - (1 + r)^-n) / r], it can determine the total savings needed before retirement. Early savings can greatly benefit from compound interest.
Step-by-step explanation:
If you want to retire at age 60 with an income stream of $50,000 for the next 30 years at a 5% return, you'll need to use the present value of annuity formula to calculate how much you need to save before retirement. The present value of annuity formula is PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is the annuity payment, r is the interest rate per period, and n is the number of periods.
For your case, PMT = $50,000, r = 0.05 (5%), and n = 30. The calculation will look like this: PV = $50,000 × [(1 - (1+0.05)^-30) / 0.05]. By doing the math, you can find the total amount you need to have saved for retirement. Since the specifics of this calculation depend on consistent and accurate use of the formula, it is important to use a calculator or financial software to get the precise amount needed.
Remember, starting to save and invest early in life can greatly increase the benefits of compound interest. For a well-diversified stock portfolio, assuming a 7% annual return over inflation can turn an initial investment into a much larger sum over time. So, the sooner you save, the greater the potential for growth.