Question

In December Corey took out a 1000-dollar loan with monthly interest rate 0.7 percent. In order to pay back the loan, Corey has been paying $87.17 a month since January. Explain why the sequence defined recursively x0=1000 and xn=1.007(xn-1) for positive n describes the balance of Corey's debt throughout the repayment of the loan.