To determine the required contributions that Derek needs to make to his retirement account, we can break down the problem into several parts. Let's identify the values for PMT, N, i/y, PV, and FV for each relevant period of Derek's retirement savings plan.
1. Understanding the Timeline
- Contributions from age 26 to 65: This is a period of 39 years (N = 39) where Derek is making contributions into the retirement account.
- No contributions from age 65 to 71: Derek will not make any deposits or withdrawals during these 6 years.
- Withdrawals starting at age 72 until 85: He plans to withdraw $122,877 annually for 14 years.
- Final balance of $1.25 million at age 85: After the last withdrawal, he wants to have $1.25 million remaining.
2. Future Value Calculation at Age 85
First, we can establish the withdrawal period. At age 71, the account must have enough to allow him to withdraw for 14 years and leave him with $1.25 million at age 85.
Let’s start with the amount he needs at age 72 to be able to withdraw $122,877 for 14 years and have $1.25 million left:
- Calculating FV of Withdrawals:
- For annual withdrawals of $122,877 for 14 years, with an interest rate of 6%:
- \( N = 14 \)
- \( i/y = 6% \)
- \( PMT = -122,877 \) (cash outflow)
- \( FV = 1,250,000 \) (cash left after last withdrawal)
Now we need to find PV (the amount required at the start of the withdrawal phase at age 72).
Using the calculator:
- Enter \( N = 14 \)
- Enter \( i/y = 6 \)
- Enter \( PMT = -122,877 \)
- Enter \( FV = 1,250,000 \)
Calculate PV: This value will tell us how much is needed in the account at age 72.
3. Calculate Contributions from Age 26 to 65
Now, we will take the PV (amount needed at age 72) and find out the annual contributions Derek needs to make from age 26 to age 65.
- Set up the values:
- The amount needed in the retirement account at age 65 (this will be the PV we calculated).
- The future value must then be calculated back to the age 26, to find out how much he will need to contribute from age 26 to age 65, while assuming no value is added during the years he is not funding the account (age 65 to age 71).
- Calculate the future value of this amount, letting it grow from age 65 to age 71 with a rate of 6% for 6 years.
Let’s denote:
- \( PV \text{ (from the previous calculation at age 72)} \)
- Now, find how much he needs to save from age 26 to age 65.
- Using the same formula to find out the contributions:
- \( N = 39 \)
- \( i/y = 6% \)
- \( PV = 0 \) (starting point)
- \( FV = \text{Amount calculated as PV required at age 72} \)
Now, enter these values (where PMT needs to be calculated):
- \( N = 39 \)
- \( i/y = 6% \)
- \( PV = 0 \)
- \( FV = PV \text{ needed at age 72}\)
Summary of Steps
- Calculate \( PV \) needed at age 72 for 14 years of $122,877 withdrawals and $1.25 million remaining after the last withdrawal.
- Then calculate necessary contributions needed annually from age 26 to age 65 to achieve the future value calculated in step 1.
Conclusion
This is how you would use the PMT function on your calculator, breaking it down into manageable steps for each age component of Derek's retirement plan.
1 answer