QuestionYou have just turned 23 years of age and accepted your first job. However, you would like to retire at 59 years of age Having paid attention in your business courses, you have calculated that you will need to save million dollars by a 59 to retire comfortably. How much must you put into your retirement savings account each year (at the end of the year) between now and age 59 (assume an interest rate of annually)?
You must put \\square$ into your retirement savings account each year.
(Round the final answer to cent as needed. Keep all decimal places as you work through the problem.)
Studdy Solution
STEP 1
1. You are currently 23 years old.
2. You plan to retire at 59 years old.
3. You need to save \$2 million by the time you retire.
4. The annual interest rate is 5%.
5. Contributions are made at the end of each year.
6. We are trying to find the annual contribution required.
STEP 2
1. Determine the number of years until retirement.
2. Use the future value of an annuity formula.
3. Solve for the annual contribution.
STEP 3
Determine the number of years until retirement.
You plan to retire at age 59, and you are currently 23 years old. Therefore, the number of years until retirement is:
STEP 4
Use the future value of an annuity formula.
The future value of an annuity formula is:
Where:
- is the future value of the annuity (\$2,000,000).
- \( P \) is the annual payment (what we are solving for).
- \( r \) is the annual interest rate (5% or 0.05).
- \( n \) is the number of years (36).
STEP 5
Solve for the annual contribution .
Rearrange the formula to solve for :
Substitute the known values into the equation:
Calculate the denominator:
Subtract 1:
Now calculate :
You must put \$ \(\boxed{16,555.08}\) into your retirement savings account each year.
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