Jiefei takes out a loan for $$13,899\mathrm{.}60.$ The term of the loan is $8$ years, and he will make weekly payments. The interest rate on the loan is $9\mathrm{.}075\%$ compounded bi$-$weekly.

a$)$ What is the effective interest rate per payment period?

b$)$ If Jiefei is going to repay the loan with level payments, what is the weekly payment amount?

c$)$ Fill in the first $3$ rows of the loan amortization table.

d$)$ What would the nominal interest rate $($compounded bi$-$weekly$)$ have to be if the weekly $($level$)$ payment amounts were $$38\mathrm{.}72?$

e$)$ If instead of level payments, Jiefei repays the loan $($with the original interest rate$)$ with level repayment of principal $($plus interest$),$ fill in the first $3$ rows of the amortization table.