Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.1 Sequences - 11.1 Assess Your Understanding - Page 828: 83

The person (Phil) owes $\$ 18,058.03$ after making the first payment.

We substitute $B_0 $ into $B_n$ in order to compute $B_1$. Therefore, $B_1=1.005 B_{1-1}-534.47 \\ =1.005 B_0-534.47 \\=(1.005)(18500)-534.47 \\= \$ 18,058.03$ We find that the person (Phil) owes $\$ 18,058.03$ after making the first payment.