Answer:
19 years
Step-by-step explanation:
The attached spreadsheet shows the balance will be zero at the beginning of year 19, when the last $10,423.27 is withdrawn from the account.
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One could argue that the "nearest year" is year 18, when the balance after the withdrawal is less than $10,000.
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In the attached spreadsheet, the ending balance is 1.082 times the beginning balance (after deposits and withdrawals), which is the ending balance of the year before (after deposits).
In year 1 the beginning balance has 100,000 added. In year 2, the ending balance has 55,000 added. In year 4 and every year after, the beginning balance as 20,000 subtracted.
