QUESTION $2.(25$p$)$ Ahmet wants to get a loan to buy a house. Therefore, he plans to make a $10-$year agreement with bank A$.$ Bank A has proposed a yearly interest rate of $(20+Y)\%,$ compounded quarterly, for a loan of $(2,000,000+x{Y}^{**}10000)TL,$ which is going to be paid monthly. Ahmet accepted the conditions and used the loan. He started to make his payments in full, with equal payments.

a$)$ Calculate the monthly $($Annual: A$)$ payment based on the interest rate offered by bank A$.$

b$)$ How much did Ahmet pay for $5$ years $($calculate the paid amount at the end of five years$)?$ How much debt does he have left if he paid his payments for $5$ years $($calculate the remaining amount at the end of five years$)?$

c$)$ At the end of the $5$th year, Ahmet, who received an offer of $(1\mathrm{.}25-0.xY)\%$ per month from bank A$,$ determined that it would be more logical to pay off the remaining debt with this loan. In this context, considering that the remaining debt $($the value you found in option $b)$ will be paid at a rate of $(1\mathrm{.}25-0.xY)\%$ for the remaining $5$ years, find the amount of monthly payment according to the new condition.