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Tutorial Exercise

Cook Security Systems has a $$37,500$ line of credit, which charges an annual percentage rate of prime rate plus $4\%.$ The starting balance on October $1$ was $$9,400.$

On October $4$ they made a payment of $$1,300.$ On October $13$ the business borrowed $$2,800,$ and on October $19$ they borrowed $$4,500.$ If the current prime rate is $9\%,$ what is the new balance?

Step $1$

The new balance of the account will be found using the previous balance, finance charge, loans, and any payments. The previous balance, loans, and payments are given, so the finance charge must be found. The finance charge is calculated using the average daily balance and the periodic rate.

To find the average daily balance, we must first determine the dates and number of days for each different unpaid balance. The beginning date for each unpaid balance is the date at which some activity occurred. The end date is the day prior to the next activity. The number of days refers to the number of days that will have the same unpaid balance.

The starting balance on October $1$ was $$9,400.$ This is the unpaid balance until the first activity on the account, a payment of $$1,300$ made on October $4.$ Therefore, the starting balance spans October $1-3,$ a period of $3$ days.

The next activity on the account occurred on October $13$ when $$2,800$ was borrowed. Therefore, the unpaid balance after the $$1,300$ payment spans October $4$ through $12,$ a period of days.

The final activity on the account occurred on October $19$ when $$4,500$ was borrowed. Therefore, the unpaid balance after borrowing $$2,800$ spans October $13$ through $,$ a period of $q,$ days.

The unpaid balance after borrowing $$4,500$ will span the rest of October. Recall there are $31$ days in October, so this unpaid balance spans October $19$ to $31,$ a period of $$ days.