Question

Gary has just retired, and has 500000 dollars in his retirement account. The account will earn interest at an annual rate of 5 percent, compounded monthly. At the end of each month, Gary will withdraw a fixed amount to cover his living expenses. Gary wants his savings to last exactly 30 years. How much money can he withdraw each month? (Give your answer in dollars, correct to the nearest cent.) monthly withdrawal: 1719.5 Incorrect: Your answer is incorrect. What is the maximum amount that Gary can withdraw each month if he wants his savings to last indefinitely? monthly withdrawal:

Answer 1

Answer:

If it wants to withdraw for 30 years the monthly withdrawlas will be of 2,684.10

If it wants to last indefinitely it will be of 2,083.33 dollars

Explanation:

Annuity of 30 years with monthly withdrawals:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $500,000.00

time 360 (30 years x 12 months)

rate 0.0041667 (rannual rate of 5% divided by 12 months per year)

$500000 \div \frac{1-(1+0.0041667)^{-360} }{0.0041667} = C$

C  $ 2,684.108

perpetuity:

monthly rate:

5% / 12 = 0,0041666666

500,000 x 0.004166666 = C = 2.083,33 dollars per month