Question
In: Finance
James and his wife would like to retire in 23 years. Upon retirement they want to...
James and his wife would like to retire in 23 years. Upon
retirement they want to spend the first 10 years traveling around
the world. To travel in the style they are accustomed they will
require $65,000 in each of the 10 years. Their first payment of
$65,000 will be 23 years from today and there will be 10 total
yearly payments of $65,000. After the years of traveling they then
want to live in a small retirement village in Charleston. For
living expenses they would like to receive yearly income of $50,000
per year in each of the next 25 years after they finish traveling
(a total of 25 yearly $50,000 payments with their first payment
beginning the year after their quit traveling).
In order to save up for these expenses, assume that Jamed and
his wife plan to deposit the same amount of money for the next 15
years (with the first deposit being one year from today) in an
account paying 9% interest compounded annually (they don’t want to
be burdened with saving money the last few years before they
retire). Calculate the amount of their annual deposits so that when
they receive their last $50,000 payment there will be a zero
balance in the account.
Solutions
Expert Solution
Step 1 Computation of Cash flows required
| Year | Required Cash Flow | PVF/PVAF @9% | PV of Cash Flows |
| 23 | 65000 | 0.1378 | 8,955.79 |
| 24 to 32 | 65000 | 0.8260 | 53,692.17 |
| 33 | 50000 | 0.0582 | 2,910.02 |
| 34 to 57 | 50000 | 0.5649 | 28,246.41 |
| 93,804.39 |
Amount of deposits to be made Each year up to Year 15 = PV of Cash Flows required / PVAF @ 9% for Year 15
= 93804.39/ 8.0607
= 11637.27
Cross verfication
| Year | Opening Bal | Deposit | Int @ 9% | Closing Balance |
| 1 | $0.00 | $ 11,637.27 | $0.00 | $ 11,637.27 |
| 2 | $ 11,637.27 | $ 11,637.27 | $1,047.35 | $ 24,321.89 |
| 3 | $ 24,321.89 | $ 11,637.27 | $2,188.97 | $ 38,148.13 |
| 4 | $ 38,148.13 | $ 11,637.27 | $3,433.33 | $ 53,218.74 |
| 5 | $ 53,218.74 | $ 11,637.27 | $4,789.69 | $ 69,645.69 |
| 6 | $ 69,645.69 | $ 11,637.27 | $6,268.11 | $ 87,551.08 |
| 7 | $ 87,551.08 | $ 11,637.27 | $7,879.60 | $ 107,067.94 |
| 8 | $ 107,067.94 | $ 11,637.27 | $9,636.11 | $ 128,341.33 |
| 9 | $ 128,341.33 | $ 11,637.27 | $11,550.72 | $ 151,529.32 |
| 10 | $ 151,529.32 | $ 11,637.27 | $13,637.64 | $ 176,804.23 |
| 11 | $ 176,804.23 | $ 11,637.27 | $15,912.38 | $ 204,353.88 |
| 12 | $ 204,353.88 | $ 11,637.27 | $18,391.85 | $ 234,382.99 |
| 13 | $ 234,382.99 | $ 11,637.27 | $21,094.47 | $ 267,114.73 |
| 14 | $ 267,114.73 | $ 11,637.27 | $24,040.33 | $ 302,792.33 |
| 15 | $ 302,792.33 | $ 11,637.27 | $27,251.31 | $ 341,680.91 |
| Year | Opening Bal | Usage | Int @ 9% | Closing Balance |
| 16 | $ 341,680.84 | $0.00 | $30,751.28 | $ 372,432.11 |
| 17 | $ 372,432.11 | $0.00 | $33,518.89 | $ 405,951.00 |
| 18 | $ 405,951.00 | $0.00 | $36,535.59 | $ 442,486.59 |
| 19 | $ 442,486.59 | $0.00 | $39,823.79 | $ 482,310.39 |
| 20 | $ 482,310.39 | $0.00 | $43,407.93 | $ 525,718.32 |
| 21 | $ 525,718.32 | $0.00 | $47,314.65 | $ 573,032.97 |
| 22 | $ 573,032.97 | $0.00 | $51,572.97 | $ 624,605.94 |
| 23 | $ 624,605.94 | $65,000.00 | $56,214.53 | $ 615,820.47 |
| 24 | $ 615,820.47 | $65,000.00 | $55,423.84 | $ 606,244.32 |
| 25 | $ 606,244.32 | $65,000.00 | $54,561.99 | $ 595,806.31 |
| 26 | $ 595,806.31 | $65,000.00 | $53,622.57 | $ 584,428.87 |
| 27 | $ 584,428.87 | $65,000.00 | $52,598.60 | $ 572,027.47 |
| 28 | $ 572,027.47 | $65,000.00 | $51,482.47 | $ 558,509.94 |
| 29 | $ 558,509.94 | $65,000.00 | $50,265.89 | $ 543,775.84 |
| 30 | $ 543,775.84 | $65,000.00 | $48,939.83 | $ 527,715.66 |
| 31 | $ 527,715.66 | $65,000.00 | $47,494.41 | $ 510,210.07 |
| 32 | $ 510,210.07 | $65,000.00 | $45,918.91 | $ 491,128.98 |
| 33 | $ 491,128.98 | $50,000.00 | $44,201.61 | $ 485,330.59 |
| 34 | $ 485,330.59 | $50,000.00 | $43,679.75 | $ 479,010.34 |
| 35 | $ 479,010.34 | $50,000.00 | $43,110.93 | $ 472,121.27 |
| 36 | $ 472,121.27 | $50,000.00 | $42,490.91 | $ 464,612.19 |
| 37 | $ 464,612.19 | $50,000.00 | $41,815.10 | $ 456,427.28 |
| 38 | $ 456,427.28 | $50,000.00 | $41,078.46 | $ 447,505.74 |
| 39 | $ 447,505.74 | $50,000.00 | $40,275.52 | $ 437,781.26 |
| 40 | $ 437,781.26 | $50,000.00 | $39,400.31 | $ 427,181.57 |
| 41 | $ 427,181.57 |
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