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Calculate the period and interest rate (opportunity cost in %) of a consumer purchase-rental plan, described as below.

You want to play the saxophone and thus sign up for a purchase rental program. The deal is:

The price tag amount of the saxophone is $1,865. You get a 20% discount if you instantly pay off the balance on the purchase date.

If not, credit loan terms are: no price discount will be provided, zero down payment needed today, interest free during the first 6 months, and then 1.5% interest per month after.

Installment loan payments are $48 per month, by the end of month.

And an extra $6 per month for the account maintenance fee, by the end of month.

a) How many months will it take you to pay off the whole deal?

b) Adding to your consideration that the $6 per month account-maintenance-fee is also another part of monthly cost for the loan plan deal, and the "after-20%-discount net price" as the present value of your opportunity cost for choosing to purchase on credit (from the perspectives of both you and the vendor, the present value of the saxophone as of today is its net cash price, not the full price tag amount), then what will be the annualized percentage rate APR of your opportunity cost for the whole deal period? In other words, if you choose not to pay cash at discounted price today but to accept the credit purchase plan instead, how high the annual percentage cost you will be subject to?