Assume that five months from today you plan to make the first of several quarter
ID: 2742408 • Letter: A
Question
Assume that five months from today you plan to make the first of several quarterly deposits into an account that pays an APR of 5.5% with monthly compounding. Your first deposit will equal $500, each of your subsequent quarterly deposits will grow by 1% each, and your final quarterly deposit will occur two years and eight months from today. From this account you plan to make semiannual withdrawals beginning three years and one month from today. Subsequent semiannual withdrawals will shrink by 2% each and your final withdrawal will occur five years and seven month from today.
a. What is the size your first withdrawal? b. If your withdrawals were all the same size rather than shrinking, would your first withdrawal be larger or smaller than your answer in part a? Assume nothing else changes.
Explanation / Answer
First withdral is 1570.649 in normal circumstances.
b.)
Value of first withdrawl will shrink.
Deposit Withdrawls Amount accumulated Interest + Amount Amount 1 500 502.29 502.29 2 502.29 504.594 504.59 3 504.59 506.907 506.91 4 525 1031.91 1036.64 1036.64 5 0 1036.64 1041.39 1041.39 6 0 1041.39 1046.16 1046.16 7 551.25 1597.41 1604.73 1604.73 8 0 1604.73 1612.09 1612.09 9 0 1612.09 1619.48 1619.48 10 578.8125 2198.29 2208.36 2208.36 11 0 2208.36 2218.49 2218.49 12 0 2218.49 2228.65 2228.65 13 607.7531 2836.41 2849.41 2849.41 14 0 2849.41 2862.47 2862.47 15 0 2862.47 2875.59 2875.59 16 638.1408 3513.73 3529.83 3529.83 17 0 3529.83 3546.01 3546.01 18 0 3546.01 3562.26 3562.26 19 670.0478 4232.31 4251.71 4251.71 20 0 4251.71 4271.2 4271.20 21 0 4271.20 4290.77 4290.77 22 703.5502 4994.32 5017.21 5017.21 23 0 5017.21 5040.21 5040.21 24 0 5040.21 5063.31 5063.31 25 738.7277 5802.04 5828.63 5828.63 26 0 5828.63 5855.34 5855.34 27 0 5855.34 5882.18 5882.18 28 775.6641 6657.84 6688.36 6688.36 29 0 6688.36 6719.02 6719.02 30 0 6719.02 6749.81 6749.81 31 814.4473 7564.26 7598.93 7598.93 32 0 7598.93 7633.76 7633.76 33 0 7633.76 7668.74 7668.74 34 0 7668.74 7703.89 7703.89 35 0 7703.89 7739.2 7739.20 36 0 7739.20 7774.67 7774.67 37 0 1570.649 7774.67 6239.66 6239.66 38 0 6239.66 6268.26 6268.26 39 0 6268.26 6296.99 6296.99 40 0 6296.99 6325.85 6325.85 41 0 6325.85 6354.84 6354.84 42 0 6354.84 6383.97 6383.97 43 0 1492.116 6383.97 4921.11 4921.11 44 0 0 4921.11 4943.67 4943.67 45 0 0 4943.67 4966.32 4966.32 46 0 0 4966.32 4989.09 4989.09 47 0 0 4989.09 5011.95 5011.95 48 0 0 5011.95 5034.92 5034.92 49 0 1417.51 5034.92 3640.49 3640.49 50 0 0 3640.49 3657.18 3657.18 51 0 0 3657.18 3673.94 3673.94 52 0 0 3673.94 3690.78 3690.78 53 0 0 3690.78 3707.69 3707.69 54 0 0 3707.69 3724.69 3724.69 55 0 1346.635 3724.69 2395.12 2395.12 56 0 0 2395.12 2406.1 2406.10 57 0 0 2406.10 2417.13 2417.13 58 0 0 2417.13 2428.21 2428.21 59 0 0 2428.21 2439.34 2439.34 60 0 0 2439.34 2450.52 2450.52 61 0 1279.303 2450.52 1182.45 1182.45 62 0 0 1182.45 1187.87 1187.87 63 0 0 1187.87 1193.31 1193.31 64 0 0 1193.31 1198.78 1198.78 65 0 0 1198.78 1204.27 1204.27 66 0 0 1204.27 1209.79 1209.79 67 0 1215.338 1209.79 0 0.00