To determine how much Derek will need in his retirement account on his 65th birthday, we can use the formula for the present value of an annuity. Here’s the step-by-step breakdown:
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Identify the variables:
- PMT: This is the payment made at the end of each period. In this case, PMT = $174,258 (the amount Derek wants to withdraw each year).
- N: This is the total number of withdrawals/periods. Since Derek is withdrawing from his 66th birthday to his 85th birthday, he will be making withdrawals for 20 years (85 - 66 + 1).
- i/y: This is the interest rate per period. Since the interest rate is 5.00%, we will enter 5.
- FV: The future value is not applicable here since we are determining the present value for a series of payments. You can set this to 0.
- PV: This is what we are trying to calculate, the present value of the annuity.
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Values for the finance calculator:
- N = 20 (the number of years Derek will withdraw).
- PMT = -$174,258 (the payment amount should be entered as a negative because it’s a cash outflow).
- i/y = 5 (the interest rate per year).
- FV = 0 (no future value to consider in this scenario).
Summary of Input:
- N = 20
- PMT = -174258
- i/y = 5
- FV = 0
After entering these values into the finance calculator, you should compute for PV which will give you the amount Derek needs in his retirement account on his 65th birthday.
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