Math HW Question

[Rei-Kuromiya]

I need help solving the following:

Mr. Tong puts away $500 per month for 10 years. After 10 years, he decides to withdraw $1000 per month. How long will it take to deplete the account (if the interest rate stays the same?

So far I've assumed this is a an annuity problem, so I set up the equation:
A= 500 [91+0.093/12)^120 -1] / (0.093/12)

and got A= $98,415.40

For the second part of the problem, I have to figure out how many years it will take for $98,415.40 to reduce to $0. How do I figure this out correctly?

 

[Denis]

Mr. Tong puts away $500 per month for 10 years. After 10 years, he decides to withdraw $1000 per month. How long will it take to deplete the account (if the interest rate stays the same?
So far I've assumed this is a an annuity problem, so I set up the equation:
A= 500 [91+0.093/12)^120 -1] / (0.093/12)
and got A= $98,415.40

Be careful, please:
the problem should state the interest rate; 9.3% compounded monthly;
your A= 500 [91+0.093/12)^120 -1] / (0.093/12) should be: A= 500 [1+0.093/12)^120 -1] / (0.093/12);
however, your A= $98,415.40 is CORRECT!

To calculate number of months that $1000 can be withdrawn:
Ai / [1 - 1/(1 + i)^n] = w
A = 98415.4
i = .093/12
w = 1000
n = number of months

Solve for n