Chapter 12.1, Problem 81AYU

Credit Card Debt John has a balance of $\$3000$ on his Discover card, which charges $1\%$ interest per month on any unpaid balance from the previous month. John can afford to pay $100 toward the balance each month. His balance each month after making a $\$100$ payment is given by the recursively defined sequence

$B_0=\$3000B_n=1.01B_{n-1}-100$.

Determine John's balance after making the first payment. That is, determine $B_1$.