You have a total of $289,416 in your retirement savings. You want to withdraw $2,500 from your account at the end of every month for living expenses and expect to earn 4.6 percent per year on your money, compounded monthly. How long will it be until you run out of money

You will be able to withdraw $2,500 for 153 months or 12 years, 9 months. The last withdrawal (154th withdrawal) will be smaller, around $782 only.

Explanation:

We can use the present value of an ordinary annuity formula to determine how long it will take to empty the account.

present value of annuity = payment x [1 - 1/(1 + i)ⁿ] / i

289,416 = 2,500 x [1 - 1/(1 + 0.00383333)ⁿ] / 0.00383333

289,416 / 2,500 = [1 - 1/(1 + 0.00383333)ⁿ] / 0.00383333

115.7664 = [1 - 1/(1 + 0.00383333)ⁿ] / 0.00383333

115.7664 x 0.00383333 = 1 - 1/1.00383333ⁿ

0.443770814 = 1 - 1/1.00383333ⁿ

1/1.00383333ⁿ = 1 - 0.443770814

1/1.00383333ⁿ = 0.556229185

1 / 0.556229185 = 1.00383333ⁿ

1.797820081 = 1.00383333ⁿ

n = log 1.797820081 / log 1.00383333 = 0.254746227 / 0.001661611345 = 153.3128 months

You will be able to withdraw $2,500 for 153 months or 12 years, 9 months. The last withdrawal will be smaller, around $782 only.

a.