Question

Brady and Sons uses accounts receivable as collateral to borrow money for operations and payroll when revenues are low. If the company borrows $300,000 now at an interest rate of 12% per year compounded monthly and the rate increases to 15% per year compounded weekly after 7 months, how much will the company owe at the end of one year? At the end of the year, the company will owe $ 341,773.67 isn't correct .

Answer 1

Annual interest rate = 12% compounded monthly, Monthly rate = 12%/12=1%

Hence, Value at end of 7 months = 300000*(1+1%)^7 = 300000*(1.01)^7=300000*1.0721= $321640.6

New interest rate will be 15% compounded weekly hence n=52

Effective interest rate = (1+i/n)^n -1

= (1+15%/52)^52 - 1

= (1+0.2885%)^52 - 1

=(1.002885)^52 -1

= 1.16158-1

= 0.16158 or 16.158%

Hence monthly interest rate = 16.158%/12 =1.3465%

Hence,  Value of $321640.6 after 5 months will be = 321640.6*(1+1.3465%)^5

= 321640.6*(1.013465)^5

= 321640.6*1.06916

= $343885.26

Hence company will owe = $343885.26