Question
In: Economics
You deposit $5,000 into an account at the end of year 0. You deposit $5,000 every...
You deposit $5,000 into an account at the end of year 0. You
deposit $5,000 every three
(3) months beginning at the end of year 1 and continuing through
the end of year 3.
You also deposit into the account an amount X starting at the end
of year 6 and repeat it
every three (3) months for a total of four (4) deposits. You
withdraw $112,160 at the
end of year 7. After the withdrawal at the end of year 7, there is
no more money in the
account. The account pays 4% compounded quarterly. What is the
amount you must
every three (3) months deposit starting at the end of year 6 (value
of X)?
Solutions
Expert Solution
The table below should help answer. 4% compounded quarterly can also be represented as 1% for each time period where each time period = 3 months.
We need to solve for x, for which see the second table below.
| amount deposited * (1.01^(28-time)) | ||||
| Year | Time (multiples of 3 months) | Amount deposited | Amount incl interest at t=28 | Amount withdrawn |
| 0 | 0 | 5,000 | 6,606 | |
| 1 | - | |||
| 2 | - | |||
| 3 | - | |||
| 1 | 4 | 5,000 | 6,349 | |
| 5 | 5,000 | 6,286 | ||
| 6 | 5,000 | 6,224 | ||
| 7 | 5,000 | 6,162 | ||
| 2 | 8 | 5,000 | 6,101 | |
| 9 | 5,000 | 6,041 | ||
| 10 | 5,000 | 5,981 | ||
| 11 | 5,000 | 5,922 | ||
| 3 | 12 | 5,000 | 5,863 | |
| 13 | - | |||
| 14 | - | |||
| 15 | - | |||
| 4 | 16 | - | ||
| 17 | - | |||
| 18 | - | |||
| 19 | - | |||
| 5 | 20 | - | ||
| 21 | - | |||
| 22 | - | |||
| 23 | - | |||
| 6 | 24 | x | ||
| 25 | x | |||
| 26 | x | |||
| 27 | x | |||
| 7 | 28 | 112160 |
Table including value of x
| amount deposited * (1.01^(28-time)) | ||||
| Year | Time (multiples of 3 months) | Amount deposited | Amount incl interest at t=28 | Amount withdrawn |
| 0 | 0 | 5,000 | 6,606 | |
| 1 | - | |||
| 2 | - | |||
| 3 | - | |||
| 1 | 4 | 5,000 | 6,349 | |
| 5 | 5,000 | 6,286 | ||
| 6 | 5,000 | 6,224 | ||
| 7 | 5,000 | 6,162 | ||
| 2 | 8 | 5,000 | 6,101 | |
| 9 | 5,000 | 6,041 | ||
| 10 | 5,000 | 5,981 | ||
| 11 | 5,000 | 5,922 | ||
| 3 | 12 | 5,000 | 5,863 | |
| 13 | - | |||
| 14 | - | |||
| 15 | - | |||
| 4 | 16 | - | ||
| 17 | - | |||
| 18 | - | |||
| 19 | - | |||
| 5 | 20 | - | ||
| 21 | - | |||
| 22 | - | |||
| 23 | - | |||
| 6 | 24 | 12,345 | 12,846 | |
| 25 | 12,345 | 12,719 | ||
| 26 | 12,345 | 12,593 | ||
| 27 |
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