A couple's IRA currently has $ 300,000. For how many months will they be able to withdraw $ 2,500 if their IRA earns .5% per month?
Answer is 183 months using an annuity immediate (First payment starts 1 month from now). Go here for the math work and proof behind that answer:
Annuity Immediate Present Value
Use the Calculate Present Value button. .5 for interest rate, 2500 for payment, and 183 for periods. If you change periods to 184 and hit calculate again, you can see the PV breaches the 300k limit, therefore, your answer is 183 months. Be advised this assumes no mortality for the collection period, meaning husband and wife are assumed to live through this period with 0% chance of death.
If you want the annuity due calc (first payment starts immediately), I can provide that too. It's on the finance page of my site, but I found a bug today that I will fix later tonight in the due lesson, and then I can provide it if you want.
The answer for an annuity due would be 182 months. All that is is (1 + i) times the annuity immediate present value. So using the annuity immediate calculator and plugging in 182 for the months, and then multiplying by 1.005 would stay under 300k, but the next month up, 183, would not.
Let me know if you have questions.
$\displaystyle 300000 = 2500a_{\overline{n; i=0.005|}}$
$\displaystyle 120 = \frac{1-1.005^{-n}}{0.005}$
$\displaystyle 0.6 = 1-1.005^{-n}$
$\displaystyle 0.4 = 1.005^{-n}$
Take natural log of both sides...
$\displaystyle -0.9163= -n(0.00499)$
$\displaystyle n = 183.72$
It takes at least 184 months to cover all payments when they are paid at the beginning of the month.
I added on to my lesson using the same link above. It shows the solving for n math work first, then plugging in values. Essentially, it does exactly what you are doing. Press Calculate N, and enter .5 for interest rate, 300000 for Present Value, and 2500 for payment. If you visited earlier this morning, and don't see it, refresh your browser and you should see the "Calculate n" button.
I do have one issue. I agree n is 183.72, but the question says how many months can they withdraw 2500. In the 184th month, a full 2500 will not be there, therefore, the answer would be 183.
Let me know if you agree.