Question

Gerry plans to make four annual deposits of $4000 into an account that pays 5.2%. The first deposit will occur in 2020. What size equal annual withdrawals can Gerry make from the account if the first withdrawal occurs in 2026 and the last occurs in 2031?

Answer: $3,794.46

please explain in detail

Answer 1

The amount is computed as shown below:

Future value of 4 deposits till 2023 is computed as follows:

Future value = Annual deposits x [ [ (1 + r)ⁿ – 1 ] / r ]

= $ 4000 x [ [ (1 + 0.052)⁴ - 1 ] / 0.052 ]

= $ 17,291.82643

Now the future value of above computed value in end of 2025 is computed as follows:

= $ 17,291.82643 x 1.052²

= $ 19,136.93348

So, the amount of withdrawal will be as follows:

Present value = Annual withdrawals x [ (1 – 1 / (1 + r)ⁿ) / r ]

$ 19,136.93348 = Annual withdrawals x [ (1 - 1 / (1 + 0.052)⁶ ) / 0.052 ] (r is taken to be 6 from year 2026 till 2031)

$ 19,136.93348 = Annual withdrawals x 5.043388699

Annual withdrawal = $ 19,136.93348 / 5.043388699

Annual withdrawal = $ 3,794.46 Approximately

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