Just saw one company's advertising:" you pay us an constant annual
amount at end of each of the next 12 years,we will repay the same
annual amount from year 13 to forever"
what interest rate are they promising?

Hi mike5-ga,

They are promising approximately 5.705% annually.

This is how the balance will accumulate at that annual rate, assuming
an annual contribution of A (figures are approximate):

Year  Balance
1      A
2      2.057051A
3      3.174407817A
4      4.355510957A
5      5.603997213A
6      6.923710858A
7      8.318715486A
8      9.793306523A
9     11.35202445A
10    12.9996688A
11    14.74131291A
12    16.58231955A

I assume there will be another year of accumulation without
contribution before the company starts paying off, that is, after you
make the last payment, you have to wait another year before the
company starts paying you.  Then at the end of year 13, the balance
would be 17.52835746A.  5.705% of this is 0.999986A, so that means
that at that rate, they can pay pretty close to A annually,
indefinitely.  If this isn't precise enough for you, please ask for a
clarification and I can come up with some more digits.

I assumed interest compounded annually.  If you assume some other
period, you will get a different answer.

I didn't solve this with algebra.  I just modeled it in a spreadsheet
program.  If you would prefer an answer with different assumptions, or
you would like details about the spreadsheet formulas, please ask for
a clarification.

--efn

---

Request for Answer Clarification by mike5-ga on 27 Mar 2003 04:50 PST

can you show me the algebraical way to solve this question?

---

Clarification of Answer by efn-ga on 27 Mar 2003 09:00 PST

Sorry, that's beyond me.  If that's what you really need, please say
so, and I will ask the editors to withdraw my answer so that another
researcher who is a better mathematician can help you.  If you want to
go that way, I would suggest you specify the problem more precisely. 
We have already seen that xarqi-ga and I interpreted it differently.

--efn

8.33%

As phrased, no interest is payable during the time of accumulation. 
After 12 years, the company will have "12A", and will have pocketed
whatever they made from investing it.  At that time, they will begin
to pay back A each year.  Therefore, the interest rate is A/12A or
8.33%.

That is, of course, if they are still in business.