calculations for withdrawal and simultaneous interest

[trimurph]

I am stuck on a problem that I believe is algebraically solvable:

If an account starts with $3000 and $200 is withdrawn annually, the account is empty in 15 years.

If there is 3% interest paid on the account annually then the time to the account reaching zero is delayed.

The first year would be (3000-200) + (3000 - 200)1.03 = value of account in second year, but the question is the correct formula to arrive at the number of years it would take with annual withdrawals of $200 for the account to reach zero?

I am sure there is an algebraic formula to derive an answer, anyone care to help out?

Thanks

 

[trimurph]

Thanks

Same as a loan payment calculation; formula:

p = ai / [1 - 1/(1+i)^n]

p = payment amount (200)
a = amount borrowed (3000)
i = interest rate (.03)
n = number of payments (?)

So solve the above for n

OK? Come back if you can't solve for n...

Now I know why I couldn't remember the formula. Thanks