Present and future value tables of $1 at 3% are presented below: Jimmy has $159,

Question

Present and future value tables of $1 at 3% are presented below:

  

  

Jimmy has $159,264 accumulated in a 401K plan. The fund is earning a low, but safe, 3% per year. The withdrawals will take place at the end of each year starting a year from now. How soon will the fund be exhausted if Jimmy withdraws $16,000 each year?

N FV $1 PV $1 FVA $1 PVA $1 FVAD $1 PVAD $1 1 1.03000 0.97087 1.0000      0.97087      1.0300      1.00000      2 1.06090 0.94260 2.0300      1.91347      2.0909      1.97087      3 1.09273 0.91514 3.0909      2.82861      3.1836      2.91347      4 1.12551 0.88849 4.1836      3.71710      4.3091      3.82861      5 1.15927 0.86261 5.3091      4.57971      5.4684      4.71710      6 1.19405 0.83748 6.4684      5.41719      6.6625      5.57971      7 1.22987 0.81309 7.6625      6.23028      7.8923      6.41719      8 1.26677 0.78941 8.8923      7.01969      9.1591      7.23028      9 1.30477 0.76642 10.1591      7.78611      10.4639      8.01969      10 1.34392 0.74409 11.4639      8.53020      11.8078      8.78611      11 1.38423 0.72242 12.8078      9.25262      13.1920      9.53020      12 1.42576 0.70138 14.1920      9.95400      14.6178      10.25262      13 1.46853 0.68095 15.6178      10.63496      16.0863      10.95400      14 1.51259 0.66112 17.0863      11.29607      17.5989      11.63496      15 1.55797 0.64186 18.5989      11.93794      19.1569      12.29607      16 1.60471 0.62317 20.1569      12.56110      20.7616      12.93794     

Explanation / Answer

Hence the fund will be exhausted in 12 year if Jimmy withdraws $16,000 each year.

Verification

Present Value of Annuity 159264 Withdrawals Per Year 16000 Present Value of Annuity/ Withdrawals Per Year: 159264/16000 9.954 PVA of $1 is 9.954 in 12th year

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