Charlie has $$10,000$ to invest for a period of $5$ years. The following three alternatives are available to him:

Account $1$ pays $3\mathrm{.}00\%$ for year $1,6\mathrm{.}00\%$ for year $2,8\mathrm{.}00\%$ for year $3,10\mathrm{.}00\%$ for year $4,$ and $11\mathrm{.}00\%$ for year $5,$ all with annual

compounding.

Account $2$ pays $11\mathrm{.}00\%$ for year $1,10\mathrm{.}00\%$ for year $2,8\mathrm{.}00\%$ for year $3,6\mathrm{.}00\%$ for year $4,$ and $3\mathrm{.}00\%$ for year $5,$ all with annual

compounding.

Account $3$ pays interest at the rate of $7\mathrm{.}56142\%$ per year for all $5$ years.

Based on the available balance at the end of year $5,$ which alternative is Charlie's best choice?

Year $5$ Balance, Alternative $1$: $

Year $5$ Balance, Alternative $2$: $

Year $5$ Balance, Alternative $3$: $

Carry all interim calculations to $5$ decimal places and then round your final answer to the nearest dollar. The tolerance is $+-5.$