Question $6$

A data analyst decided to do all design work from home and wants to create a home office. The analyst needs a new computer for $$2,500$ and printer$/$scanner for $$350.$ A vendor offers a financing option of a monthly installment of $$129$ for a period of $24$ months. First payment is due at the end of the month of purchase. The vendor will accept either a cash payment upfront or financing over $24$ months as mentioned earlier. The vendor has a value of time of $5\%$ per year. Compounding is monthly.

$[$a$]$ What is the monthly interest rate implied in the vendor's offer? That is$,$ if the analyst decides to buy in installments, what is the interest cost of borrowing from the vendor $($instead of any other source$)?$

$[$b$]$ If the analyst requested a refinancing plan over a $6-$month installment period $($still monthly payments but only for $6$ months$)$ instead of $24$ months and the vendor agrees for the same interest rate as part $[$a$]$ what would be the monthly payment be in this case?