Question

"The fund is earning a low, but safe, 3% per year. The withdrawals will take place annually starting today. How soon will the fund be exhausted if Debbie withdraws $40,000 each year?"

Answer 1

The question is missing the amount that Debbie's fund has, so I looked for similar questions and the number I found was $368,882.

we can use the present value of an annuity due formula to determine how long it will take Debbie to empty her account.

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

368,882 = (40,000 / 0.03) x {1 - [1 / (1 + 0.03)ⁿ]} x (1 + 0.03)

368,882 = 1,333,333.33 x 1.03 x {1 - [1 / (1 + 0.03)ⁿ]}

368,882 = 1,373,333.33 x {1 - [1 / (1 + 0.03)ⁿ]}

1 - [1 / (1.03)ⁿ] = 368,882 / 1,373,333.33 = 0.268603398

1 - 0.268603398 = [1 / (1.03)ⁿ]

0.731396601 = 1 / (1.03)ⁿ

1.03ⁿ = 1 / 0.731396601 = 1.367247261

n = log 1.367247261 / log 1.03 = 0.135847062 / 0.012837224 = 10.58 years

Debbie will exhaust the fund in 10.58 years. That means that Debbie will be able to withdraw $40,000 for 10 years, and then the last withdrawal will be lower.

Step-by-step explanation: