To calculate how much Mrs. Kay needs to invest each year to reach her goal, we will use the future value of annuity formula to determine the amount she needs to have saved by the time she retires, and then use the present value of annuity formula to determine how much she needs to invest each year to reach that goal. Here are the steps:
1. Determine how many years Mrs. Kay will be saving before retirement:
She plans to retire at age 60 and is currently 24 years old, so she will be saving for 60 - 24 = 36 years.
2. Determine the future value of the withdrawals she plans to make during her retirement:
Mrs. Kay wants to withdraw $120,000 per year for 40 years, beginning one year after she retires. Since the account will be earning 4.5% interest per year, we can use the future value of annuity formula:
FV = P * [(1 + r)^n - 1] / r
where FV = future value of withdrawals, P = annual withdrawal amount ($120,000), r = annual interest rate (4.5% = 0.045), and n = number of years she plans to make withdrawals (40).
FV = $120,000 * [(1 + 0.045)^40 - 1] / 0.045
FV ≈ $8,676,696
So, Mrs. Kay needs to have $8,676,696 saved by the time she retires to be able to make her desired withdrawals.
3. Determine how much she needs to invest each year to achieve that future value:
Mrs. Kay will be investing in an account that earns 7% interest per year and she plans to invest the same amount each year. Using the present value of annuity formula:
PV = FV / [(1 + r)^n - 1] / r
where PV = present value (the amount she needs to invest each year), FV = future value of the account ($8,676,696), r = annual interest rate (7% = 0.07), and n = number of years she will be saving (36).
PV = $8,676,696 / [(1 + 0.07)^36 - 1] / 0.07
PV ≈ $6,095
So, Mrs. Kay needs to invest approximately $6,095 each year in order to reach her goal of having $8,676,696 saved by the time she retires.
Mrs. Kay who is 24 years old plans to retire at the age of 60. Mrs. Kay would like to be able to withdraw $120,000 per year from her retirement account for 40 years after retirement beginning a year after her retirement. She already has $15,000 in her retirement investment account that earns 7% per year. After retirement she plans to take less risk so she will move her investment into an account that earns 4.5% per year. How much does she need to invest each year in order to reach her goal?
can you explain how you got the answer.
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