Chapter 12.1, Problem 83AYU

Car Loans Phil bought a car by taking out a loan for $\$18,500$ at $0.5\%$ interest per month. Phil's normal monthly payment is $\$434.47$ per month, but he decides that he can afford to pay $\$100$ extra toward the balance each month. His balance each month is given by the recursively defined sequence

$B_0=18,500B_n=1.005B_{n-1}-534.47$.

Determine Phil's balance alter making the first payment. That is. determine $B_1$.