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?
FV available at Year 2026:
Sum [ FV of CFs deposited ]
FV = PV (1+r)^n
| Year | Gap | CF | FVF @5.2% | FV of CFs |
| 2020 | 6 | $ 4,000.00 | 1.3555 | $ 5,421.94 |
| 2021 | 5 | $ 4,000.00 | 1.2885 | $ 5,153.93 |
| 2022 | 4 | $ 4,000.00 | 1.2248 | $ 4,899.17 |
| 2023 | 3 | $ 4,000.00 | 1.1643 | $ 4,657.01 |
| FV of CFs | $ 20,132.05 |
Amount Withdrawl = Amount available / PVAF (r%, n)
= $ 20132.05 / [ PVAF ( 5.2% , 5 ) + 1 ]
= $ 20132.05 / [ 4.3056 + 1 ]
= $ 20132.05 / 5.3056
= $ 3794.49
As the withdrawls are for 6 Years and begining from 2026 amounts to Annuity due.
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