Answer
See below
Work Step by Step
The new recursive rule is $a_1=10000\\a_2=1.0054a_{n-1}-(196+50)=1.0054a_{n-1}-246$
with $n\geq 2$
After using a graphing calculator, we see that $a_{48}=-248$. Hence, we need 47 months to repay the loan.
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