Question

Suzane is 30 years old and would like to maximize the amount she cam deposit into her retirement account, however she is limited in the amount she can deposit. The IRS limits the maximum deposit amount and she has leftover student debt that also limits her deposit rate. The IRD limit ius $18,500 today and is expected to rise by the cost of iunflation at 2.5% per year. Because of her student debt Suzanne can only deposit $6,000 per year for the first six years. On year seven she will be able to deposit the maximum allowable amunt byu the IRS into her account and is expectiung to do so for 20 consecutive years. The expected rate of return on this account is 8% per year compounded annually.

What is the maximum deposit she will be allowed by the IRS in year seven?

a. How much money will have accumulated in her account after 26 years?

b. Since she can only begin withdrawing fromn her retirement account after age 59 and since she expects to live to the average life expectance of 88 years, what is the equivalent uniform annual amount she can withdraw from this account if she expects to withdraw this account completely over her remaining life exoectancy? consider that the account continues to return 8% per year compounded annually.

Draw the cash flow diagram

Answer 1

Suzane Present Age 30 Years Student Debt limitation 6 Years Further Contribution 20 Years 56 Years Starting from today Suzane wil Invest pto the age of 56 years then after she wil withdraw the amount after 59 years. 3 Years Waiting Period Withdrwal Period From 59 Years to 88 Years 30 Years Both Inclusive) Maximum Particulars/Year ("investment is Permissibile made at the beginning of the Year) Amount Year 30 18,500.00 Year 31 18,942.50 Year 32 19.435.56 Year 33 19,922.48 Year 34 20.420.54 Year 35 20,931.05 Year 36 21,454.33 Year 37 21,990.09 Year 38 22,540.45 Year 39 23, 103.96 Year 40 23,681.56 Year 41 24,273.60 Year 42 24.880.44 Year 43 25,502.45 Year 44 26, 140.02 Year 45 26,793.52 Year 46 27.463.35 Year 47 28, 149.94 Year 48 28.853.69 Year 49 29,575.03 Year 50 30,314.40 Year 51 31,072.26 Year 52 31.849.07 Year 53 32.645.30 Year 54 33,461.43 Year 55 34.797.97 Year 56 Year 57 Year 58 Year 59 Year 50 Year 61 Year 63 Year 62 Year 64 Year 65 Year 66 Year 67 Year 68 Year 69 Year 70 Year 71 Year 72 Year 73 Year 74 Year 75 Year 76 Year 77 Year 78 Year 19 Year 80 Year 81 Year 82 Year 83 Year 84 Year 5 Year 86 Year 87 Year RS Interest at the Investment at the Withdrawls at Cumulative end of the investment at Beginning Amount of Investment at the beginning the beginning balance Year 8% the end of Year 6000 6,000.00 480.00 6,480.00 6 AND.00 COOL 12,480.00 998. 40 13,478,40 13.478.40 1947.40 1,558.27 21,036.67 21.036.67 27.036.67 2.152.93 29,199.61 29,199.61 6000 25.199.61 2.915.97 39 015.57 38,015.57 6000 44,015.57 3.521.25 47536.82 47536.87 21,454.33 68.991.15 5,519.29 74,510.44 74 510.44 21,990.69 96,501.13 7,720.09 104,221.22 1,04 221.22 22,540.45 1,26 761.67 10.140.93 1,36,902.00 1,36,902.60 23,102 96 1,60 006.57 1290053 1,22.07.09 1,72 807.09 23,681 56 1,96 488.66 15.719.09 2.12.207.75 2.12.207.75 24,273.60 2,36 481.35 18.918 51 2.55, 399.86 2,55,399.85 24,880.44 2,80, 280.31 22 422423 ,02,702.73 3,02,202.73 25,502.45 3,28,205.18 26.256.41 3 ,54,461.60 3,54,461.00 26,140 02 3,80,601.62 30,448.13 4,11,049.74 4,11049.74 26,29352 4,37 843.26 35,027.46 4,72,870.22 4,72 870.72 27,463 35 5.00 334.08 40,026.73 5.40.360.80 5,40,360.80 28.14994 5,68,510.74 45 480.86 6.13.991.60 6,13,991.60 28,853.69 6,42 845.28 51427,62 6,94,272.91 6,94,272.91 29,575.03 7,23, 847.94 57 907.83 7 ,81,755.77 7,81,755.77 30,314.40 8,12.07.18 64965.618 ,77,035.79 8,77,035.79 31,072.26 9,08,109. 72,648.64 9,90,736.70 9,80,756.70 31,849.07 10,12,605.77 81.008.46 10.93.614.23 10.93.514.23 32.645 30 11,26.259.53 90.100.76 12.16.360.29 12.16 360.29 33,46143 12,49,821.72 99,385.74 1349,807,46 13.49.807.46 34,297.97 13,84 105.42 1.10.728.43 14.94,833.86 14,94 833.55 14,94,833.86 1,19,586.71 16,14,470.57 16.14420.57 16,14,420.57 1.29. 153,65 1743.574 21 17.43.574,21 17.43.574,21 1.39.485.94 18.83.060.15 18,83060.15 154,877 22 17.28.182.93 1.38.254.63 18.66.437.56 18,66,437.55 1,54,877 22 17.11.560.34 1.36.924.83 1848.485.16 18.48 485.16 1.54,877.22 16,93,607.94 1,35488.64 18,29,095.58 18,79,096.58 154,877.22 16,74 219.36 1,33 937.55 18.08.156.90 18.08.156.90 154,877.22 16.53 229.68 1.32,262.37 17.95.542.06 17,85 542.05 154.877 22 16.30.664.83 130,453.19 17.61.118.02 17.61.118.02 1,54,877.22 16.06.240.80 1.28.499.26 17.34.740.06 17,34,740.05 154,877 22 15.79.862.84 1.26.389.03 17.06.251.87 17.06.251.87 154,877 22 15,51 374.65 1.24,109.97 16,75,184,62 16.75 484.62 154,877 22 15,20,607.40 1.21 648 9 16.42.255.99 16.42 255.99 1,54,877.22 14,87 378.77 1.18.990.30 16.06.269.07 16.05.369.07 154,877.22 14.51491.85 1 16.119.35 15.67.611.19 15,67 511.19 1.54,877.22 14,12.733.97 113.01R 72 15 25 75 15,25.752.69 154,87722 13.70.875.47 1.09,670.04 14,80,545.50 14.80 545.50 1.54,877 22 13.25.568.28 1.06.053.46 14,31,721.74 14,31,721.74 1,54,877.22 12,76,844.52 1,02 147.56 13.29.992.08 13,78.992.03 1.54.877.22 12.24. 114.86 97,929.19 13.22.044,05 13.22.044.05 154.877.22 11.67 166.83 93,373.35 12.60.540.17 12.60.540.17 1.54.877.22 11.05.562.95 88.451.04 11.94 115.99 11.M 115.99 154,877 22 10,39 238.77 83.139.10 11.22.377.87 11,22,377.87 1,54,877.22 9,67 500.05 77,400.05 10,44,900.70 10,44 900.70 1 54,877.22 9.90 023.48 71.201.88 9,61.225.35 9.61.225.35 154,877.22 8,06, 348.13 64 507 85 8,70,855.98 8,70.855.98 1.54,877.22 7,15.978.76 57 278.00 7,73.252.06 7.73.257.05 154.877.22 6.18.379.84 49.470 39 6.67,850.23 6,67 850.23 154,877 22 5.12.973.00 41,037.84 5.54.010.14 5,54 010.84 1,54,877.22 3.991R3.62 31.930.69 4 ,31,064.31 4,31,064.31 1,54,877.22 2,76, 187.09 22,094.97 2,99,282.06 2,98,282.06 1,54,877.22 1,43 404,84 11.472.39 1 ,54,877.22 1,54,877.22 1-54,877.22 -0.00 -0.00 -0.00 Formula to Calculate withdraw's 18,83,060.15

Green Period indicates the period till when suzane can invest only $6000 per Year.

withdrwal (W) = (beginning of year) PxRx (1+r)^(N-1)/(1+R)^(N)-1] 1,54,877.22 withdrwal (W) - End of Year PXRX (1+R) NM(1+R/N)-1] 167,267,40 Year Year 59 Year 60 Year 61 Year 62 Year 62 Year 64 Year 65 Year 66 Year 67 Year 68 Year 69 Year 70 Year 71 Year 72 Year 73 Year 74 Opening Bal 18.83.060.15 18,66,437 56 18,48,485.16 18,29,096.58 13.08. 156.90 17,95 542.06 17.61.118.02 17,34,740.06 17.06.251.87 16,75,484.62 16.42 255.99 16.06.369.07 15,67,611.19 15,25,752.69 14,80.545.50 14,31,721.74 13,78.992.08 13,22.044,05 12,60.540.17 11.94 115.99 11.22.377.87 10,44,900.20 9,61,225.35 8,20,855.98 7,73,257.06 6,67,850.23 5.54,010.84 4,31,064.31 2.99 282.06 1,54,877.22 interest Withdrawl 150614.8118 149315.0048 147878 8132 146327.7262 144652.5524 142843.3646 140689.4417 138779.2051 136500.1495 134038.7695 131380.4791 128509.5254 125403,8954 122060 2151 118443.6403 114537.7395 110319.3667 105763.5241 100843.214 95529 27912 89790 22947 83592 05584 7689802932 69668 47959 61860 56489 53429.0181 44320.86756 34485 14498 23962 56459 12290 17777 Closing balance 167267.3996 18,66,437.56 167267.3998 18.48.185.16 167267.3998 18,29,096.58 167267.3998 18.00, 156.90 167267.2299 1785,542.06 167267,3998 17,61,118.02 167267,3998 17.34.740.06 167267.3998 17,06,251.87 167267.3998 16,75,184.62 167267.3998 16,42,255.99 167267.3999 16,06,369.07 167267.299915.67.611.19 167267,3998 15,25,752.69 167267,3998 14.80.545.50 167267.3998 14.31.721.74 167267.3998 13,78,992.08 167267.2999 12. 22.044.05 167267.2999 12.60.540.17 167267.3998 11.94.115.99 167267,3998 11.22.377.87 1672673998 10,44,900.70 167262,2998 9,61,225.35 167267.3999 8,70,855.99 167267.3999 7,73,257,06 167267,3298 6,67,850.23 1672672908 5.54.010.84 167267,3990 4.31.064.31 167267.3998 2.98,282.00 167262,2999154,877.22 167267.2999 Year 25 Year 76 Year 77 Year 78 Year 79 Year 80 Year 81 Year 82 Year 82 Year B4 Year B5 Year RS Year 87 Year 88 0.00

Yellow Period Indicates 20 Years Period during which maximum investment permissible (with inflation) is given

Sky Blue Period indicates holding period of no investment and no withdrawal; only interest for this period is given.

Rest Dark blue period is divided into annuity of withdrawals of 30 years.