Final answer:
To retire with $1 million by the age of 65 when starting at 25 with a 10% annual return, one would need to invest a certain amount monthly using the future value of an annuity formula. Starting early and consistently investing with compound interest can significantly increase retirement savings over time.
Step-by-step explanation:
To determine how long it will take to retire with at least $1 million with an anticipated rate of return of 10%, and how much would need to be invested each month starting at age 25, we can use the future value of an annuity formula:
FV = P * [((1 + r)^n - 1) / r]
where FV is the future value, P is the monthly payment, r is the monthly interest rate, and n is the number of payments.
Assuming a 10% annual interest rate, to retire with $1 million, we will have to adjust the rate for monthly contributions:
r = 0.10 / 12
Next, we need to choose the age at which retirement is desired to calculate 'n', the number of payments. If you start saving at age 25 and plan to retire at 65, that's 40 years of investments, so:
n = 40 * 12
Plug in the values to the formula to solve for P, which will give you the monthly investment required.
Italics: Since saving early in life is crucial, according to economists, targeting around 15% of income for retirement savings is advisable. Also, the example of saving $3,000 a year and the effect of compound interest over several decades highlights the importance of starting early and consistently investing for retirement.