Present and future value tables of $1 at 3% are presented below: N FV $1 PV $1 F

Question

Present and future value tables of $1 at 3% are presented below: 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 Debbie has $235,855 accumulated in a 401K plan. 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 $50,000 each year?

Explanation / Answer

If debbie withdraws $50000 each year, deposit of $235855 with earning 3% per year will exhaust in the year in which Accumulated DF of 3% per year will come to = 235855/50000 = 4.717

Accumulated DF for 5 years = 4.579

Accumulated DF for 6 years = 5.417

So DF of year 6 is = 0.837

4.579 will recover in year 4 and rest (4.717 - 4.579) = 0.137 will recover 0.137/0.837 *12 = 2 months

So the initial amount will exhaust in 5 years and 2 months.

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