High School

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4. (8 pts)

You have gotten your first credit card and spent $1000 but have no money. Your credit card company charges you 18% interest compounded monthly.

a. After 3 months, how much money will you owe the bank? After 1 year, how much will you owe the bank? (3 pts)

b. To help pay off your $1000 debt, you get a part-time job. If you pay the credit card company a minimum payment of $25 each month, how much money would you end up paying in interest? How many payments would you have to make, and how many years will it take you to pay off the debt? (2 pts)

c. What is a credit score? How do you build a credit score? Why would it be beneficial to build a credit score? Answer in complete sentences with a minimum of one paragraph (5 sentence minimum). (3 pts)

Answer :

Final answer:

To calculate the amount of money you will owe on your credit card after a certain period of time, you can use the formula for compound interest. After 3 months, you will owe $1015 on your credit card. If you make minimum payments of $25 per month, it will take approximately 5 years and 4 months to pay off the debt, and you will end up paying about $402.40 in interest. Building a credit score involves making on-time payments, keeping credit card balances low, and having a mix of different types of credit accounts.

Explanation:

To calculate the amount of money you will owe on your credit card after a certain period of time, you can use the formula for compound interest. The formula is:

A = P(1 + r/n)^(nt)

Where:

  • A is the final amount (the amount you owe after the specified time)
  • P is the principal amount (the initial amount you spent)
  • r is the annual interest rate (in decimal form)
  • n is the number of times interest is compounded per year (in this case, monthly, so n = 12)
  • t is the number of years

a. After 3 months, you can substitute the values into the formula and calculate the amount you will owe. P = $1000, r = 18% (0.18), n = 12, and t = 3/12 (since it's 3 months). Plugging in these values, A = $1000(1 + 0.18/12)^(12*(3/12)) = $1000(1 + 0.015)^(1) = $1000(1.015) = $1015.

b. To determine how long it will take to pay off the debt by making minimum payments, you can use a credit card payoff calculator. Using the given values of a $1000 debt and a minimum payment of $25 per month, the calculator will show that it will take approximately 5 years and 4 months to pay off the debt. In this time, you will end up paying approximately $402.40 in interest.

c. A credit score is a numerical representation of an individual's creditworthiness. It is used by lenders to assess the risk of lending money to an individual. Building a credit score involves consistently making on-time payments, keeping credit card balances low, and having a mix of different types of credit accounts. Having a good credit score can be beneficial because it makes it easier to qualify for loans and get better interest rates on loans and credit cards.

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