Question

you want to retire a millionaire when you are 65. currently, you have $20,000 in savings and are 30 years old. how much will you have to save each year for the next 35 years in order to have $1,000,000? assume you earn 9% on your savings every year. round off your final answer to three digits after the decimal point. state your answer as

Answer 1

To reach a million-dollar retirement goal at age 65, starting with $20,000 at age 30, calculate the future value of the current savings at a 9% return, then use the future value of an annuity formula to find the required annual savings.

Step-by-step explanation:

To retire with a million dollars at the age of 65, starting from age 30 with $20,000 already saved, you need to calculate the additional annual savings required assuming a 9% annual return. To do so, we calculate the future value of the current savings and the future value of a series of annuities (annual savings). Using the formula for the future value of an annuity, we solve for the annuity payment (annual savings needed).

First, we calculate the future value of the current $20,000 at a 9% annual return over 35 years:

$20,000 × (1 + 0.09)^{35} = FV

Next, we use the future value of an annuity formula:

FV = P × [ ((1 + r)^n - 1) / r ]

where FV is the desired future value ($1,000,000 minus the future value of the current savings), P is the annual payment (what we're solving for), r is the annual rate of return (0.09), and n is the number of periods (35).

After substituting and solving for P, we obtain the amount that needs to be saved annually. Rounding off to three decimal places as requested, this gives us our final answer.