Go Fly a Kite has a 27500 line of credit which charges an an

Go Fly a Kite has a $27,500 line of credit which charges an annual percentage rate of prime rate plus 3.5%. Their starting balance on April 1 was $7,000. On April 10 they borrowed $5,600. On April 18 the business made a payment of $2,400, and on April 27 they borrowed $3,900. If the current prime rate is 6%, what is the new balance?

Solution

when Go Fly a Kite borrows money then its line of credit reduces and every time they borrow money they are charged an interest at an interest rate of 3.5%+6% = 9.5% per annum

on tenth april they borrowed = $ 5600

interest on 5600 would be compounded

=> A = P(1+r/n)^(nt) = 5600(1 + 9.5/100)^1 = 6132

=> interest = 6132 - 5600 = $ 532

on april 27th they borrowed = 3900

=> A = P(1+r/n)^(nt) = 3900(1 + 9.5/100)^1 = 4270.5

=> interest = 4270.5 - 3900 = $ 370.5

Opening balance was = 7000

then they borrowed 5600 , so the balance becomes = 7000+5600 = 12600

then they made a business payment of 2400 , so the new balance becomes = 12600 - 2400 = 10200

then they borrowed 3900 , so the balance becomes = 10200 + 3900 = $ 14100

go fly a kite would have to pay the amount borrowed with interest back as well

hence the new balance becomes = 14100 - 6132 - 4270.5 = $ 3697.5