Thread: Annuity Due

Steve wishes to save for his retirement by depositing 1200 at the beginning of each year for 30 years. Exactly one year after his last deposit, he wishes to being making annual level withdrawals until he has made 20 withdrawals and exhausted the savings. Find the amount of each withdrawal if the effective interest rate is 5% during the first 30 years but only 4 percent after that.

Here is what i did:
Used formula for annuity due to get ending balance of first 30 years and got. 83,712.95 I thought that that gave me the balance at the end of year 29 so i multiplied that by 5 percent and got 86,224.33. Then i used my calculator to get the pmts. I have a baII plus. and used these numbers:
n=20 i/y=4 pv = 86,224.33 fv = 0. i got a pmt of 6344.537.
thats off by about 400 dollars. i tried not taking my 83,712.95 and increasing it by 5 percent but i was still off. what did i do wrong?

Thank you!

83,712.95 is balance at end of year 30. So leave it alone!

And this will result in payments of 5,922.83

how come its for the end of 30 years. i thought since it started at time 0, 30 years would be year 29, wouldn't it? what am i missing?

The formula you used took take care of the last year's interest,
so you used the "beginning of period" formula.

Try it out on something real simple, like 1000 per year for 3 years, 10% rate;
you'll see what I mean...

Code:

0    1000.00       .00    1000.00
1    1000.00    100.00    2100.00
2    1000.00    210.00    3310.00
3        .00    331.00    3641.00

Uh. So it takes to the next year. Thats makes it a lot clearer. Thank you for your help