SOLUTION: My question is about an annuity. How do we solve the annuity formula for time? Now, scott8148 has been great with reversing a formula with logarithmic conversions, but this seems

Algebra ->  Finance -> SOLUTION: My question is about an annuity. How do we solve the annuity formula for time? Now, scott8148 has been great with reversing a formula with logarithmic conversions, but this seems      Log On


   

Question 319724: My question is about an annuity. How do we solve the annuity formula for time? Now, scott8148 has been great with reversing a formula with logarithmic conversions, but this seems pretty complex.
The standard annuity formula reads as such:
w=%28P%281%2Br%2Fn%29%5E%28nt-1%29%28r%2Fn%29%29+%2F+%28%281%2Br%2Fn%29%5E%28nt%29-1%29
This would answer the question, "If some money is withdrawn from the principle every month for 20 years, how much could be withdrawn?"
Fair enough, but what about a question such as, "Jan wants to withdraw $800 every month until her account reaches zero. How long will it be before her account reaches zero?" This is assuming that the amount withdrawn would be large enough to break past the interest and cut into the capital, of course.
Thanks so much for any reply,
Charlie Bass
Abilene, TX
cfbass@yahoo.com
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
You again, Charlie?

multiplying by n/r ___ wn%2Fr+=%28P%281%2Br%2Fn%29%5E%28nt-1%29%29+%2F+%28%281%2Br%2Fn%29%5E%28nt%29-1%29

multiplying by %28%281%2Br%2Fn%29%5E%28nt%29-1%29 ___

subtracting %28%281%2Br%2Fn%29%5E%28nt%29%29%28wn%2Fr%29%29 ___

factoring ___

dividing by %28%28P%281%2Br%2Fn%29%5E%28-1%29%29+-+%28wn%2Fr%29%29 ___

taking log ___

dividing by n%28log%28%281%2Br%2Fn%29%29%29 ___

hope this works for you