Question

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 $9,700. On october 4 they made a payment of $1,600. On october 13 the business borrowed $2,100, and on october 19 they borrowed $4,800. If the current prime rate is 8%, what is the new balance (in $)? (round your answer to the nearest cent. )

Answer 1

First, we need to calculate the interest rate that Cook Security Systems is being charged on their line of credit:
Interest rate = prime rate + 4%
Interest rate = 8% + 4%
Interest rate = 12%

Next, we can calculate the interest charged on the starting balance of $9,700$ for the period between October 1 and October 4:
Interest = (balance x interest rate x time) / 365
Interest = (9700 x 0.12 x 3) / 365
Interest = $94.01

The balance after the payment on October 4 is:
Balance = $9,700 - $1,600 - $94.01 = $8,005.99

Next, we can calculate the interest charged on the balance of $8,005.99 for the period between October 4 and October 13:
Interest = (balance x interest rate x time) / 365
Interest = (8005.99 x 0.12 x 9) / 365
Interest = $236.53

The balance after the borrowing on October 13 is:
Balance = $8,005.99 + $2,100 + $236.53 = $10,342.52

Finally, we can calculate the interest charged on the balance of $10,342.52 for the period between October 13 and October 19:
Interest = (balance x interest rate x time) / 365
Interest = (10342.52 x 0.12 x 6) / 365
Interest = $201.01

The balance after the borrowing on October 19 is:
Balance = $10,342.52 + $4,800 + $201.01 = $15,343.53

Therefore, the new balance (rounded to the nearest cent) is $\$15,343.53$.