excel pv function

Equation: 26000 x R^12 - 538.46 x R x (R^12 - 1) / (R - 1)
where R = 1 + 8.9%/12

Solution:

Let R be 1 + 8.9%/12 = 1.007416666...
the balance after 1 month = 26000 x R
the balance after 2 month = [26000 x R - 538.46] x R
= 26000 x R^2 - 538.46 x R
the balance after 2 month = [26000 x R^2 - 538.46 x R - 538.46] x R
= 26000 x R^3 - 538.46 x R^2 - 538.46 x R
......
......
......
thus the balance after 12 month
= 26000 x R^12 - 538.46 x R^11 - 538.46 x R^10 + ... - 538.46 x R
= 26000 x R^12 - 538.46 x R x (1 + R + R^2 + ... + R^11)
= 26000 x R^12 - 538.46 x R x (R^12 - 1) / (R - 1)
= 21629.11556

pv is used to evaluate present value when the future value is known.
In your case the present value is known and you want to find the future value
so you should use fv instead of pv

2012-11-23 16:55:12 補充：
If you use fv the logic will be simple.
Interest rate = 8.9% / 12
12 payments in 1 year
Monthly payment = $538.42625 (I use more precise number to avoid rounding error)
Present value = $26,000
The value 1 year later can be found by
=fv(8.9%/12,12,-538.45625,26000)

2012-11-23 16:55:55 補充：
If you insist to use pv then you have to go through some thought process first
Imagine 1 year has passed and we want to know the balance as today. So we know the future value is $0 in 4 years time and we want to know the present value
=pv(8.9%/12,48,-538.45625,0)