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June 4th, 2015, 05:18 AM   #1
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Short Annuity

Abe opens a savings account, which generously pays interest of 1% monthly.

Abe makes 12 monthly deposits, the first being d dollars; these increase by
10% monthly, i.e. the 2nd deposit being 1.10d, the 12th being (1.10^11)d.

During the following year, beginning 1 month after his last deposit, Abe
makes monthly withdrawals, the first being 100 dollars.

These withdrawals increase by a constant 50 dollars per month, i.e.:
150 dollars in 2nd month, ..., 650 dollars in 12th month.

The final withdrawal of 650 dollars brings the account to .00 (or ZIP!).

Praytell, what is the value of d?
Please report such with the first 12 digits following the decimal point.

Thank you.

Last edited by Denis; June 4th, 2015 at 05:23 AM.
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June 7th, 2015, 05:59 AM   #2
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d = $185.85
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June 7th, 2015, 06:31 AM   #3
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185.849135979785
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