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Like many college students, Susan applied for and received a credit card with an annual percentage rate (APR) of 18%. She purchased a new DVD player for $350. At the end of the month, her credit card statement indicated a minimum monthly payment of $10.

Assuming Susan makes her payment when she sees her statement at the end of each month and doesn't charge anything else, approximately how many months would it take her to completely pay off the DVD player? Assume the credit card company compounds interest at the end of each month.

Answer :

Final answer:

It's complex to calculate the exact time for Susan to pay off her DVD player due to compound interest and ongoing monthly payments without a spreadsheet or financial program. However, understanding the basics of compound interest lets you know that it'll likely take longer than you might anticipate.

Explanation:

This problem requires understanding compound interest and the concept of a loan repayment plan. Compound interest is calculated by compounding the interest onto the capital, which is the original balance Susan borrowed to purchase the DVD player.

The formula for compound interest is: A = P(1 + r/n)^(nt), where A is the amount owed (principal plus interest), P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

However, in this case, Susan is also repaying her loan by making minimum monthly payments ($10), so her owed balance decreases each month. It is not straightforward to calculate the exact time to repay it completely due to the balance reduction and ongoing accrual of interest, hence, this could be approximated using spreadsheets or specialized financial software programs.

Learn more about Compound Interest here:

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