In order to save for his retirement, Dale Falcinelli makes the first of 8 equal
ID: 2732379 • Letter: I
Question
In order to save for his retirement, Dale Falcinelli makes the first of 8 equal annual deposits into an investment on June 6, 2014.He believes the investment will always earn 10% a year. The last deposit will be made on June 6, 2021. The deposits must be of sufficient size to enable Mr. Falcinelli to make 30 equal annual withdrawals of $80,000 starting on June 6, 2026. Assume that he makes the 8 deposits as planned and makes the first two $80,000 withdrawals in 2026 and 2027. On the evening of June 6, 2027, Mr. Falcinelli makes a horrifying discovery: the investment has been yielding only 5% since June 6, 2017. Fully expecting to still live another 28 years, he knows he must drastically cut back on his lavish life style. What's the maximum constant amount he can withdraw for each of the remaining 28 years, starting June 6, 2028 if the interest rate continues to stay at 5%?
Explanation / Answer
let investing amount each year= $100 s.no first of 8 equal annual deposits into an investment opening balance deposit Amount Interest Rate @ 10% closing balance 1 June 6, 2014 0.00 100.00 10.00 110.00 2 June 6, 2015 110.00 100.00 21.00 231.00 3 June 6, 2016 231.00 100.00 33.10 364.10 4 June 6, 2017 364.10 100.00 46.41 510.51 5 June 6, 2018 510.51 100.00 61.05 671.56 6 June 6, 2019 671.56 100.00 77.16 848.72 7 June 6, 2020 848.72 100.00 94.87 1043.59 8 June 6, 2021 1043.59 100.00 114.36 1257.95 9 June 6, 2022 1257.95 0.00 125.79 1383.74 10 June 6, 2023 1383.74 0.00 138.37 1522.12 11 June 6, 2024 1522.12 0.00 152.21 1674.33 12 June 6, 2025 1674.33 0.00 167.43 1841.76 13 June 6, 2026 1841.76 0.00 184.18 2025.94 The deposits must be of sufficient size to enable Mr. Falcinelli to make 30 equal annual withdrawals of $80,000 starting on June 6, 2026 =80000*30 2400000.00 so value of investment 2025.94 point equal to 2400000.00 value of annual equal installment =2400000/2025.94*100 value of annual equal installment 118463.70 by fill this value of above table s.no first of 8 equal annual deposits into an investment opening balance deposit Amount Interest Rate @ 10% closing balance 1 June 6, 2014 0.00 118463.70 11846.37 130310.07 2 June 6, 2015 130310.07 118463.70 24877.38 273651.14 3 June 6, 2016 273651.14 118463.70 39211.48 431326.32 4 June 6, 2017 431326.32 118463.70 54979.00 604769.02 5 June 6, 2018 604769.02 118463.70 72323.27 795556.00 6 June 6, 2019 795556.00 118463.70 91401.97 1005421.66 7 June 6, 2020 1005421.66 118463.70 112388.54 1236273.90 8 June 6, 2021 1236273.90 118463.70 135473.76 1490211.35 9 June 6, 2022 1490211.35 0.00 149021.14 1639232.49 10 June 6, 2023 1639232.49 0.00 163923.25 1803155.74 11 June 6, 2024 1803155.74 0.00 180315.57 1983471.31 12 June 6, 2025 1983471.31 0.00 198347.13 2181818.44 13 June 6, 2026 2181818.44 0.00 218181.84 2400000.29 table after change of 5% yield after june,2017 s.no first of 8 equal annual deposits into an investment opening balance deposit Amount Interest Rate closing balance 1 June 6, 2014 @10% 0.00 118463.53 11846.35 130309.88 2 June 6, 2015@10% 130309.88 118463.53 24877.34 273650.75 3 June 6, 2016@10% 273650.75 118463.53 39211.43 431325.71 4 June 6, 2017@10% 431325.71 118463.53 54978.92 604768.16 5 June 6, 2018 @ 5% 604768.16 118463.53 36161.58 759393.27 6 June 6, 2019 @ 5% 759393.27 118463.53 43892.84 921749.64 7 June 6, 2020 @ 5% 921749.64 118463.53 52010.66 1092223.82 8 June 6, 2021 @ 5% 1092223.82 118463.53 60534.37 1271221.72 9 June 6, 2022 @ 5% 1271221.72 0.00 63561.09 1334782.81 10 June 6, 2023 @ 5% 1334782.81 0.00 66739.14 1401521.95 11 June 6, 2024 @ 5% 1401521.95 0.00 70076.10 1471598.04 12 June 6, 2025 @ 5% 1471598.04 0.00 73579.90 1545177.94 13 June 6, 2026 @ 5% 1545177.94 0.00 77258.90 1622436.84 total value of investment 1622436.84 first two $80,000 withdrawals in 2026 and 2027. 160000.00 balance of investment 1462436.84 balance 28 equal withdrwals will be 52229.89