What is annuity factor?

the PV ordinary annuity "factor" is: [(1 - (1 / (1 + i)^n)) / i] from the formula...PVoa = PMT [(1 - (1 / (1 + i)^n)) / i] rearranged to solve for pmt....PMT = PVoa / [(1 - (1 / (1 + i)^n)) / i] <the PV factor is the divisor here the FV ordinary annuity "factor" is: [((1 + i)^n - 1) / i] from the formula...FVoa = PMT [((1 + i)^n - 1) / i] rearranged to solve for pmt...PMT = FVoa / [((1 + i)^n - 1) / i] <the FV factor is the divisor here, this is the formula represented in your question above..rent = FV / [((1 + i)^n - 1) / i]<divisor aka FV factor...

An annuity is when you withdraw money at regular intervals from an investment till the investment is dwindled to zero or to a pre-determined value. Note that what's left in the investment continues to earn money as per the future value equation of FV = PV * ( 1 + R )^t. There are tables of numbers for the mathematically inept. What he is saying is that if a principle of $102,452 which if deposited at 10% interest for four years would've been $150,000 if you did not with draw anything, you could withdraw $32,321 at end of each year for four years before the account balance became 0. Now this is solved with the summation of a geometric sequence but is often rewritten into what is called the ordinary annuity equation. What he's presenting as the annuity factor is the future value of the principle had you not withdrawn any money from it. This is an unusual way of doing it because it's usually the factor for the present value as in the first two links (equation for it in the first link). You can get the values he used by dividing more common present value versions from the first two links by 1.10^4 to project it to a future value. It doesn't really make sense to do this but people do as shown in the third link. To confuse matters, they don't tell you if they're using a present value or future value version. Now, I myself would just go back to basics and use the results of the summation of a geometric sequence which gives you: P * ( 1 + R )^n = X * ( 1 - ( 1 + R )^n ) / ( 1 - ( 1 + R ) ) Therefore for his example, the payment would be: X = P * ( 1 + R )^n * ( 1 - ( 1 + R ) ) / ( 1 - ( 1 + R )^n ) .: X = 102,452 * 1.10^4 * ( 1 - 1.10 ) / ( 1 - 1.10^4 ) X = 32,320.61 Note that the 102,452 * 1.10^4 corresponds with his $150,000 future value equivalent and the rest is the reciprocal of his future value annuity factor so you could say his annuity factor is: future value annuity factor = ( 1 - ( 1 + R )^n ) / ( 1 - ( 1 + R ) ) which can be simplified to: future value annuity factor = ( ( 1 + R )^n - 1 ) / R .: for his example: future value annuity factor = ( ( 1 + 0.10 )^4 - 1 ) / 0.10 = 4.6410 The equation for the present value annuity factor which makes more sense but is equally un-needed mathematically is in the first link. Remember the annuity factor is really only for those who can't do math, they're just making up tables to replace dozens of equations when if they knew math they would understand that all those equations were really just the summation of a geometric sequence equation in various forms. I always get thumbs down on this cause many people are taught all those equations such as the ordinary annuity equation and never realized they are all just one equation to begin with. The irony is that the summation of a geometric sequence is taught in junior high, just seldom understood.