The company you work for will deposit $150 at the end of each month into your retirement fund....

Let,

• r = interest rate = 12% / 12 = 1% per month
• n = number of saving months = 25 * 12 = 300
• k = number of spending months = 30 * 12 = 360
• PV = present value of annuity
• FV = future value of annuity
• p = employer contribution = $150
• q = your contribution = ?

Your savings for retirement must be equal to the value of your spending stream. Therefore, the future value of savings is equal to the present value of spending:

{eq}FV(Saving \ n \ periods)=PV(Spending \ k \ periods)\\ Saving*\frac{(1+r)^{n}-1}{r}=Spending*\frac{1-(1+r)^{-k}}{r}\\ (p+q)*\frac{(1+r)^{n}-1}{r}=Spending*\frac{1-(1+r)^{-k}}{r}\\ (150+q)*\frac{(1+0.01)^{300}-1}{0.01}=2,000*\frac{1-(1+0.01)^{-360}}{0.01}\\ q=-\$46.51\\ {/eq}

Since the number you need to deposit is negative, you can withdraw $46.51 per month before retirement.