Question
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A couple is saving for retirement with three different accounts. The table below shows the current...
A couple is saving for retirement with three different accounts. The table below shows the current balances in their accounts, along with their yearly contribution, and the yearly return on each account. The couple will retire in 23.00 years and pool the money into a savings account that pays 3.00% APR. They plan on living for 25.00 more years and making their yearly withdrawals at the beginning of the year. What will be their yearly withdrawal?
| Account | Balance | Yearly Contribution | APR |
|---|---|---|---|
| Fidelity Mutual Fund | $22,364.00 | $1,000.00 | 7.00% |
| Vanguard Mutual Fund | $189,616.00 | $10,000.00 | 7.00% |
| Employer 401k | $305,616.00 | $15,000.00 | 6.00% |
Solutions
Expert Solution
Solution:
In order to calculate their yearly withdrawl, first we will calculate total money that couple will have after 23 years and this will be total future value of 3 accounts:
| Computation of Future Value - Fidelity Mutual Fund | |||||
| Year | Opening Balance | Investment | rate of Interest ( r ) | Interest Amount (Opening balance * r) | Closing Balance (Opening balance + Investment + Interest) |
| 1 | $22,364.00 | $1,000.00 | 7% | $1,565.48 | $24,929.48 |
| 2 | $24,929.48 | $1,000.00 | 7% | $1,745.06 | $27,674.54 |
| 3 | $27,674.54 | $1,000.00 | 7% | $1,937.22 | $30,611.76 |
| 4 | $30,611.76 | $1,000.00 | 7% | $2,142.82 | $33,754.58 |
| 5 | $33,754.58 | $1,000.00 | 7% | $2,362.82 | $37,117.41 |
| 6 | $37,117.41 | $1,000.00 | 7% | $2,598.22 | $40,715.62 |
| 7 | $40,715.62 | $1,000.00 | 7% | $2,850.09 | $44,565.72 |
| 8 | $44,565.72 | $1,000.00 | 7% | $3,119.60 | $48,685.32 |
| 9 | $48,685.32 | $1,000.00 | 7% | $3,407.97 | $53,093.29 |
| 10 | $53,093.29 | $1,000.00 | 7% | $3,716.53 | $57,809.82 |
| 11 | $57,809.82 | $1,000.00 | 7% | $4,046.69 | $62,856.51 |
| 12 | $62,856.51 | $1,000.00 | 7% | $4,399.96 | $68,256.46 |
| 13 | $68,256.46 | $1,000.00 | 7% | $4,777.95 | $74,034.42 |
| 14 | $74,034.42 | $1,000.00 | 7% | $5,182.41 | $80,216.83 |
| 15 | $80,216.83 | $1,000.00 | 7% | $5,615.18 | $86,832.00 |
| 16 | $86,832.00 | $1,000.00 | 7% | $6,078.24 | $93,910.24 |
| 17 | $93,910.24 | $1,000.00 | 7% | $6,573.72 | $101,483.96 |
| 18 | $101,483.96 | $1,000.00 | 7% | $7,103.88 | $109,587.84 |
| 19 | $109,587.84 | $1,000.00 | 7% | $7,671.15 | $118,258.99 |
| 20 | $118,258.99 | $1,000.00 | 7% | $8,278.13 | $127,537.12 |
| 21 | $127,537.12 | $1,000.00 | 7% | $8,927.60 | $137,464.71 |
| 22 | $137,464.71 | $1,000.00 | 7% | $9,622.53 | $148,087.24 |
| 23 | $148,087.24 | $1,000.00 | 7% | $10,366.11 | $159,453.35 |
| Computation of Future Value - Vanguard Mutual Fund | |||||
| Year | Opening Balance | Investment | rate of Interest ( r ) | Interest Amount (Opening balance * r) | Closing Balance (Opening balance + Investment + Interest) |
| 1 | $189,616.00 | $10,000.00 | 7% | $13,273.12 | $212,889.12 |
| 2 | $212,889.12 | $10,000.00 | 7% | $14,902.24 | $237,791.36 |
| 3 | $237,791.36 | $10,000.00 | 7% | $16,645.40 | $264,436.75 |
| 4 | $264,436.75 | $10,000.00 | 7% | $18,510.57 | $292,947.33 |
| 5 | $292,947.33 | $10,000.00 | 7% | $20,506.31 | $323,453.64 |
| 6 | $323,453.64 | $10,000.00 | 7% | $22,641.75 | $356,095.39 |
| 7 | $356,095.39 | $10,000.00 | 7% | $24,926.68 | $391,022.07 |
| 8 | $391,022.07 | $10,000.00 | 7% | $27,371.54 | $428,393.62 |
| 9 | $428,393.62 | $10,000.00 | 7% | $29,987.55 | $468,381.17 |
| 10 | $468,381.17 | $10,000.00 | 7% | $32,786.68 | $511,167.85 |
| 11 | $511,167.85 | $10,000.00 | 7% | $35,781.75 | $556,949.60 |
| 12 | $556,949.60 | $10,000.00 | 7% | $38,986.47 | $605,936.07 |
| 13 | $605,936.07 | $10,000.00 | 7% | $42,415.53 | $658,351.60 |
| 14 | $658,351.60 | $10,000.00 | 7% | $46,084.61 | $714,436.21 |
| 15 | $714,436.21 | $10,000.00 | 7% | $50,010.53 | $774,446.74 |
| 16 | $774,446.74 | $10,000.00 | 7% | $54,211.27 | $838,658.02 |
| 17 | $838,658.02 | $10,000.00 | 7% | $58,706.06 | $907,364.08 |
| 18 | $907,364.08 | $10,000.00 | 7% | $63,515.49 | $980,879.56 |
| 19 | $980,879.56 | $10,000.00 | 7% | $68,661.57 | $1,059,541.13 |
| 20 | $1,059,541.13 | $10,000.00 | 7% | $74,167.88 | $1,143,709.01 |
| 21 | $1,143,709.01 | $10,000.00 | 7% | $80,059.63 | $1,233,768.64 |
| 22 | $1,233,768.64 | $10,000.00 | 7% | $86,363.81 | $1,330,132.45 |
| 23 | $1,330,132.45 | $10,000.00 | 7% | $93,109.27 | $1,433,241.72 |
| Computation of Future Value - Employer 401K | |||||
| Year | Opening Balance | Investment | rate of Interest ( r ) | Interest Amount (Opening balance * r) | Closing Balance (Opening balance + Investment + Interest) |
| 1 | $305,616.00 | $15,000.00 | 6% | $18,336.96 | $338,952.96 |
| 2 | $338,952.96 | $15,000.00 | 6% | $20,337.18 | $374,290.14 |
| 3 | $374,290.14 | $15,000.00 | 6% | $22,457.41 | $411,747.55 |
| 4 | $411,747.55 | $15,000.00 | 6% | $24,704.85 | $451,452.40 |
| 5 | $451,452.40 | $15,000.00 | 6% | $27,087.14 | $493,539.54 |
| 6 | $493,539.54 | $15,000.00 | 6% | $29,612.37 | $538,151.92 |
| 7 | $538,151.92 | $15,000.00 | 6% | $32,289.11 | $585,441.03 |
| 8 | $585,441.03 | $15,000.00 | 6% | $35,126.46 | $635,567.49 |
| 9 | $635,567.49 | $15,000.00 | 6% | $38,134.05 | $688,701.54 |
| 10 | $688,701.54 | $15,000.00 | 6% | $41,322.09 | $745,023.63 |
| 11 | $745,023.63 | $15,000.00 | 6% | $44,701.42 | $804,725.05 |
| 12 | $804,725.05 | $15,000.00 | 6% | $48,283.50 | $868,008.55 |
| 13 | $868,008.55 | $15,000.00 | 6% | $52,080.51 | $935,089.07 |
| 14 | $935,089.07 | $15,000.00 | 6% | $56,105.34 | $1,006,194.41 |
| 15 | $1,006,194.41 | $15,000.00 | 6% | $60,371.66 | $1,081,566.08 |
| 16 | $1,081,566.08 | $15,000.00 | 6% | $64,893.96 | $1,161,460.04 |
| 17 | $1,161,460.04 | $15,000.00 | 6% | $69,687.60 | $1,246,147.64 |
| 18 | $1,246,147.64 | $15,000.00 | 6% | $74,768.86 | $1,335,916.50 |
| 19 | $1,335,916.50 | $15,000.00 | 6% | $80,154.99 | $1,431,071.49 |
| 20 | $1,431,071.49 | $15,000.00 | 6% | $85,864.29 | $1,531,935.78 |
| 21 | $1,531,935.78 | $15,000.00 | 6% | $91,916.15 | $1,638,851.93 |
| 22 | $1,638,851.93 | $15,000.00 | 6% | $98,331.12 | $1,752,183.05 |
| 23 | $1,752,183.05 | $15,000.00 | 6% | $105,130.98 | $1,872,314.03 |
Total money will be transferred to saving account afte 23 years = $159,453.35 + $1,433,241.72 + $1,872,314.03
= $3,465,009.10
Now this money will be invested in saving account at 3% interest rate and every year couple withdraw equal amout say a at the beginnig of year so that in 25 years balance in saving account will be zero.
Therefore
Yearly withdrawl = $3,465,009.10 / Cumulative pv factor for 25 period of immediate annuity at 3%
= $3,465,009.10 / 17.93554212 = $193,192.33
Therefore yearly withdrawl amount comes at $193,192.33
jeff jeffy answered 1 year agoRelated Solutions
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