Counting Annual Annuity Withdrawals from Age 60 to 89

Summary

The question concerns the number of annual withdrawals needed to fund retirement from age 60 through age 89. Since both birthdays mark withdrawal dates, the sequence includes one withdrawal at age 60 and one at each subsequent birthday through age 89, for 30 withdrawals. Counting the listed ages inclusively resolves why the calculation uses 30 periods rather than 29 elapsed years between the first and final withdrawal dates.

The reply demonstrates this with a simple inclusive count. It does not calculate the required starting balance, explain annuity timing conventions, or discuss how the 6% return is applied between withdrawals. Those details matter when valuing the cash flows: the first withdrawal occurs immediately at retirement, so the situation is an annuity due rather than a sequence whose first payment arrives one year later.

Key ideas

• Counting ages 60 through 89 inclusively gives 30 withdrawal dates.
• The 29-year gap between the first and last birthdays does not mean there are only 29 payments.
• A withdrawal made on the retirement date makes the cash-flow pattern an annuity due.
• The reply clarifies the period count but does not derive the present value.

Tags

# Finding the period for annuities


# Finding the period for annuities












I've got a question relating to annuities which I'm stuck on.

You intend to retire when you are 60 and predict you will die when you are 90. You want 50,000 a year for a comfortable retirement, and you plan to get this money through an investment account. The account pays a return of 6%. On your 60th birthday, you will withdraw $50,000. You will continue to withdraw this amount until your 89th birthday. At that point there will be no money left in your account. How much money will you need to have saved from now until you are 60?

I understand the mathematics behind this, but what confuses me is that the instructor set n = 30 when doing the calculations. This is confusing to me - I understand that there are a total of 30 withdrawals but shouldn't n be 29 as there are 29 years from your 60th birthday until your 89th?

Cheers

## Answer by Bob Jansen (score 1)

https://quant.stackexchange.com/a/61738

No, it comes to 30:

```
~ R
> length(60:89)
[1] 30
```

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