Question
In: Finance
An amount of $3,000 is deposited into Fund X, which earns an annual effective rate of...
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An amount of $3,000 is deposited into Fund X, which earns an annual effective rate of 8%. At the end of each year, the interest earned plus an additional $150 is withdrawn from the fund. At the end of the twentieth year, the fund is depleted. The annual withdrawals of interest and principal are deposited into Fund Y, which earns an annual effective rate of 10%.
Determine the accumulated value of Fund Y at the end of year 20. Justify your answer
Solutions
Expert Solution
This can be better shown using the below table.
| Year | Opening Balance of fund X | Amount Deposited In fund X | Interest Earned @ 8% | Fixed Withdrawl Amount from Fund X | Total Withdrawl From Fund X | Closing balance of fund X | Opening Balance of Fund Y | Withdrawl Reinvested | Interest earned @ 10% | Closing balance |
| 1 | - | 3,000.0 | 240.0 | 150.0 | 390.0 | 2,850.0 | - | - | - | - |
| 2 | 2,850.0 | - | 228.0 | 150.0 | 378.0 | 2,700.0 | - | 390.0 | 39.0 | 429.0 |
| 3 | 2,700.0 | - | 216.0 | 150.0 | 366.0 | 2,550.0 | 429.0 | 378.0 | 80.7 | 887.7 |
| 4 | 2,550.0 | - | 204.0 | 150.0 | 354.0 | 2,400.0 | 887.7 | 366.0 | 125.4 | 1,379.1 |
| 5 | 2,400.0 | - | 192.0 | 150.0 | 342.0 | 2,250.0 | 1,379.1 | 354.0 | 173.3 | 1,906.4 |
| 6 | 2,250.0 | - | 180.0 | 150.0 | 330.0 | 2,100.0 | 1,906.4 | 342.0 | 224.8 | 2,473.2 |
| 7 | 2,100.0 | - | 168.0 | 150.0 | 318.0 | 1,950.0 | 2,473.2 | 330.0 | 280.3 | 3,083.5 |
| 8 | 1,950.0 | - | 156.0 | 150.0 | 306.0 | 1,800.0 | 3,083.5 | 318.0 | 340.2 | 3,741.7 |
| 9 | 1,800.0 | - | 144.0 | 150.0 | 294.0 | 1,650.0 | 3,741.7 | 306.0 | 404.8 | 4,452.5 |
| 10 | 1,650.0 | - | 132.0 | 150.0 | 282.0 | 1,500.0 | 4,452.5 | 294.0 | 474.6 | 5,221.1 |
| 11 | 1,500.0 | - | 120.0 | 150.0 | 270.0 | 1,350.0 | 5,221.1 | 282.0 | 550.3 | 6,053.4 |
| 12 | 1,350.0 | - | 108.0 | 150.0 | 258.0 | 1,200.0 | 6,053.4 | 270.0 | 632.3 | 6,955.8 |
| 13 | 1,200.0 | - | 96.0 | 150.0 | 246.0 | 1,050.0 | 6,955.8 | 258.0 | 721.4 | 7,935.1 |
| 14 | 1,050.0 | - | 84.0 | 150.0 | 234.0 | 900.0 | 7,935.1 | 246.0 | 818.1 | 8,999.2 |
| 15 | 900.0 | - | 72.0 | 150.0 | 222.0 | 750.0 | 8,999.2 | 234.0 | 923.3 | 10,156.6 |
| 16 | 750.0 | - | 60.0 | 150.0 | 210.0 | 600.0 | 10,156.6 | 222.0 | 1,037.9 | 11,416.4 |
| 17 | 600.0 | - | 48.0 | 150.0 | 198.0 | 450.0 | 11,416.4 | 210.0 | 1,162.6 | 12,789.1 |
| 18 | 450.0 | - | 36.0 | 150.0 | 186.0 | 300.0 | 12,789.1 | 198.0 | 1,298.7 | 14,285.8 |
| 19 | 300.0 | - | 24.0 |
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