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# John has a balance of $3000 on his credit card that charges 1% interest per month on any unpaid balance. 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 $$ B_0= $3000,\quad B_n=1.01B_{n-1}-100 $$ (a) Determine John’s balance after making the first payment. That is, determine $B_1$. (b) Using a graphing utility, determine when John’s balance will be below $2000. How many payments of$100 have been made? (c) Using a graphing utility, determine when John will pay off the balance. What is the total of all the payments? (d) What was John’s interest expense?

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VerifiedStep 1

1 of 3#### a.

$B_{1}=1.01(B_{0})-100==1.01(3000)-100=2930\\\\$$B_{1}=\$2930.$

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