It is now February 1, 2049 and you have just retired. To fully enjoy your retirement, you would like to be able to withdraw an amount from your account of $75,000 for the first years of retirement. You have accumulated vacation and sick leave which is added to your departure bonus and which can cover your expenses for the first 3 years of retirement. Then, the first withdrawal of $75,000 is made on February 1, 2052 and the last on February 1, 2059. Thereafter, an amount of $40,000 per year will be sufficient until February 1, 2069. The first withdrawal of $40,000 will be made on February 1, 2060 and the last on February 1, 2069. Animal lover, you would also like to leave an amount of $1,000 per year (first payment on 1 January 1, 2065) in perpetuity at the local animal shelter for which you worked volunteering all these years. The assumed interest rate on your investments throughout your retirement is 5% per year. b) How much money do you need to have amassed by the time you retire (the 1st February 2049) to finance all these needs?
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likesAnswer to a math question It is now February 1, 2049 and you have just retired. To fully enjoy your retirement, you would like to be able to withdraw an amount from your account of $75,000 for the first years of retirement. You have accumulated vacation and sick leave which is added to your departure bonus and which can cover your expenses for the first 3 years of retirement. Then, the first withdrawal of $75,000 is made on February 1, 2052 and the last on February 1, 2059. Thereafter, an amount of $40,000 per year will be sufficient until February 1, 2069. The first withdrawal of $40,000 will be made on February 1, 2060 and the last on February 1, 2069. Animal lover, you would also like to leave an amount of $1,000 per year (first payment on 1 January 1, 2065) in perpetuity at the local animal shelter for which you worked volunteering all these years. The assumed interest rate on your investments throughout your retirement is 5% per year. b) How much money do you need to have amassed by the time you retire (the 1st February 2049) to finance all these needs?
4.61. Calculate the present value of the $75,000 annual withdrawals from February 1, 2052, to February 1, 2059 (8 payments annuity).
2. Calculate the present value of the $40,000 annual withdrawals from February 1, 2060, to February 1, 2069 (10 payments annuity).
3. Calculate the present value as of February 1, 2049, of the perpetuity of $1,000 starting on January 1, 2065. Calculate the present value on January 1, 2065, first and then discount it back to February 1, 2049.
4. Sum up all the present values to determine the total amount needed by February 1, 2049.
1. Present value of $75,000 annual withdrawals = $418,737.46
2. Present value of $40,000 annual withdrawals = $180,589.54
3. Present value of $1,000 annual perpetuity = $9,162.23
Adding these values gives the total amount needed by February 1, 2049 to finance all the retirement needs:
Therefore, the total amount needed is approximately $608,489.23."