Our High School Math teacher, Mr. Warren, is retiring next year when he reaches 65. He put this question to us:
When he retires he intends to withdraw, from his retiremend account, an annual payment, at the end of each year, of $50,000 for 25 years. If his $50,000 is adjusted for annual inflation rate of 3% and he earns 6% ,compounded annually, on his retirement fund, how much money should he have in his retirement fund? Thanks for any help.
This is basically the PV of an ordinary annuity with a couple minor adjustments:
1) Since his payments are adjusted for inflation of 3% per year and the interest he earned is 6% per annum, we have to find the net of the two rates as follows:
1.06 / 1.03 =2.91262%. We also have adjust his first payment by 3% inflation rate as follows:
$50,000 / 1.03 =$48,543.69.
Now we can use the ordinary annuity formula to find the PV of all his 25 payments as follows:
PV=P{(1 + R)^N - 1]*[1 + R]^-N * R^-1}=PV OF $1 PER PERIOD.
PV=48,543.69{[(1 +0.0291262) ^25 - 1] * [1 + 0.0291262]^-25 * 0.0291262^-1}
=$853,587.68. This is PV of his annuity.
2)-
We can also sum up all his future payments, using summation formula, on any good calculator such as Wlofram/ Alpha engine as follows:
∑[50000*1.03^n / 1.06^(n+1)], n=0 to 24 =$853,587.68. And here is the link to W/A:
http://www.wolframalpha.com/input/?i=%E2%88%91%5B50000*1.03%5En+%2F+1.06%5E(n%2B1)%5D,+n%3D0+to+24
Thanks a lot for this. One small question I have: Can we do amortization on this annuity such as a loan or morthage?
Do you mean amortization schedule? Certainly, especially if you use a spreadsheet like Excel. Keep in mind that the annuity earns interest @ 6%, while his annual payments increase by 3% per year. So that his payments would increase as $50,000, $51,500, $53,045, $54,636.35.....etc.
