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More than 1 billion credit cards are in circulation in the United States. Many credit cards charge an annual percentage rate (APR) of 18.3%. The average American carries a credit card debt of approximately $8,600. Analyze and answer the following questions related to these facts and using what you learned in this lesson. 1. For a certain credit card, the total amount, A ,that a customer owes is given by the following formula. In the formula, P is the starting balance and n is the number of months of debt, assuming interest is compounded monthly. Suppose you begin with a credit card debt of
More than 1 billion credit cards are in circulation in the United States. Many credit cards charge an annual percentage rate (APR) of 18.3%. The average American carries a credit card debt of approximately $8,600. Analyze and answer the following questions related to these facts and using what you learned in this lesson. 1. For a certain credit card, the total amount, A ,that a customer owes is given by the following formula. In the formula, P is the starting balance and n is the number of months of debt, assuming interest is compounded monthly. Suppose you begin with a credit card debt of $1000. After one year, you will owe $ _______. (Round your answer to the nearest cent and enter only the number.) A=P(1.015)^n 2. How long will it take for the total amount owed to reach $1300? a.about18 months b.about 15 months c.about 20 months d.about 12 months 3. An unpaid debt with compounding interest grows in time. Suppose your debt starts out at $3500 and that in the next five years, the debt can grow with interest. Your goal is to pay off the accumulated debt in five years. To compute your monthly payment during the five years, use the formula shown. In the formula, M is the monthly payment, P is the principal (initial amount of the loan), n is the number of periods (in this case 60 months), and r is the interest rate per period (which is APR divided by 12 expressed as a decimal). If the credit card has an APR of 18.3%., what monthly payment will pay off the debt in exactly five years? 4. For a certain credit card, given a starting balance of P and an ending balance of A, the function below gives the number of months n that have passed, assuming that no payments or additional purchases occurred during that time. Suppose you started with a debt of $1000 and now owe $1210.26. The debt has been building for ___ months. Round to the nearest whole month. (Hint: First simplify the numerator by hand, using the properties of logarithms. Then use a calculator to evaluate the numerator divided by the denominator to find the value of n.)