Walnut just bought a new cracker for $$100,000\mathrm{.}00.$ To pay for the cracker, the company took out a loan that requires Walnut to pay the bank a special payment of $$51,000\mathrm{.}00$ in $2$ months and also make regular monthly payments forever. The first regular payment is expected in $1$ month and is expected to be $$204\mathrm{.}57.$ All subsequent regular payments are expected to increase by a constant rate each month forever. The interest rate on the loan is $0\mathrm{.}89$ percent per month. What is the monthly growth rate of the regular payments expected to be$?$

$0\mathrm{.}42\%($plus or minus $1bps)$

$0\mathrm{.}48\%($plus or minus $1bps)$

$0\mathrm{.}20\%($plus or minus $1bps)$

$0\mathrm{.}69\%($plus or minus $1bps)$

none of the answers are within $1bps$ of the correct answer