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Answer :
Final Answer:
Like many college students, Lisa applied for and got a credit card that has an annual percentage rate (APR) of 15%. The first thing she did was buy a new DVD player for $350. At the end of the month her credit card statement said she only needed to make a minimum monthly payment of S10. Assume Lisa makes her payment when she sees her statement at the end of each month. If Lisa doesn't charge anything else and only makes the minimum monthly payments approximately how many months would it take her to completely pay off the DVD player? Assume that the credit card company compounds interest at the end of each month.
The correct option is
(C) 32.6 months
Explanation:
In the given scenario, Lisa has a credit card with an annual percentage rate (APR) of 15%. She used it to buy a $350 DVD player and was informed that she needed to make a minimum monthly payment of $10. If Lisa only pays the minimum amount each month it will take her approximately 32.6 months to pay off the DVD player completely.
To calculate this we first need to find out how much she will be paying towards interest and how much she will be paying towards the principal (the actual amount of the DVD player). The interest is calculated by multiplying the APR by the balance owed at the end of each month. Since Lisa only makes the minimum payment the balance will decrease each month but the interest will still be calculated on the original balance. The rest of her payment goes towards paying off the principal.
To find out how much interest Lisa will be paying each month we use the formula:
Interest = (APR/12) x Current Balance
For the first month Lisa's current balance is $350 (the cost of the DVD player). So the interest for the first month is (0.15/12) x 350 = $4.38.
This means that out of the $10 she pays, $4.38 goes towards interest and $5.62 goes towards paying off the principal. After the first month Lisa's balance is now $344.38 ($350 - $5.62). We repeat this process for each month until the balance reaches zero.
It will take Lisa approximately 32.6 months to completely pay off the DVD player because that's when her balance will be close enough to zero (less than $0.01) that the credit card company will consider it paid off.
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