Clarabelle borrowed $$120,000$ at a nominal interest rate of $6\mathrm{.}0\%$

compounded monthly. She agrees to make end of month payments for $10$ years.

She missed payments $59$ and $60.$ The lender penalizes her by raising the interest

rate to $7\mathrm{.}8\%$ compounded monthly for the remaining $5$ years $($i$.$e$.$ for all payments

after month $60)$ of the loan term. What new level monthly payments are required to

pay off the loan assuming she pays off the loan in the original $10$ year time frame? answer: $$1,444\mathrm{.}58$ please show work