Mathematics 86 Online
OpenStudy (anonymous):

AJ takes out a small business loan of 15500 dollars at a nominal rate of interest of 7.4 percent convertible quarterly. One year later, he repays 3500 dollars. Two years after that, the bank wants to sell AJ's loan to another institution. How much does AJ owe at that time?

OpenStudy (anonymous):

since it's convertible quarterly you use a compound interest formula using the rate/4. So the amount owed after one year (four quarters), will be: P (1 + r/4)^4 where P = the principal and r = .074

OpenStudy (anonymous):

hey md, any luck?

OpenStudy (anonymous):

hi, thanks for helping me... i converted the interest as u said but im having trouble to set up the equation..

OpenStudy (anonymous):

i have it as follows : 15500=3500+x(1.0185)^12 and im solving for x.

OpenStudy (anonymous):

hey md

OpenStudy (anonymous):

hmmm, well, you're looking for the total amount that is owed on the load after 3 years

OpenStudy (anonymous):

after the first year, 15500*(1 - .074/4)^4 is left on the loan

OpenStudy (anonymous):

at that time, AJ pays 3500, and you have another equation

OpenStudy (anonymous):

... with a new principal. two years after that time, the total amount on the load is: ((15500*(1-.074/4)^4) - 3500) * (1+ .074/4)^8 (since AJ now owes two more years - 8 quarters - at the same rate but new principal)