Final answer:
Suman can calculate the annual amount needed for retirement savings using the future value annuity formula, considering a 9 percent rate of return over 25 years. By understanding compound interest, she can maximize her savings growth, aiming for a substantial retirement fund.
Step-by-step explanation:
Suman is looking to save for her retirement and wants to know how much she needs to invest at the end of each year to reach her goal of $600,000 by the time she turns 55. Given a 9 percent rate of return, and using the formula for the future value of an annuity, we can calculate this amount for her. Since Suman is currently 30 and plans to retire at 55, she has 25 years to make these investments.
Calculating the Annual Investment
To find the constant annual amount Suman must save, we use the future value annuity formula FV = Pmt * [(1 + r)^n - 1] / r, where FV is the future value, Pmt is the payment at the end of each period, r is the rate of return per period, and n is the total number of periods. Plugging in Suman's details:
- FV = $600,000
- r = 9% or 0.09
- n = 25 years
By rearranging the formula to solve for Pmt, we get:
Pmt = FV / [(1 + r)^n - 1] / r)
After solving, Suman will find out the exact amount she needs to save annually to reach her goal by age 55.
Understanding the power of compound interest is critical in saving for retirement. An initial investment grows over time as interest is earned on the amount saved and on the interest that has been previously earned. Starting to save early can result in a significant amount of wealth due to compound interest, potentially allowing one to be in the top 10% of American households in terms of accumulated wealth for retirement.