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Edgar accumulated $5,000 in credit card debt. If the interest rate is 20% per year and he does not make any payments for 2 years, how much will he owe on this debt in 2 years with monthly compounding

User Nuvious
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2 Answers

6 votes

Final answer:

To calculate the compounded credit card debt of $5,000 after 2 years at a 20% annual interest rate with monthly compounding, the formula for compound interest is used. The final amount will be greater than the original debt, highlighting the impact of compound interest on unpaid credit card balances.

Step-by-step explanation:

The student has asked how much they will owe on a $5,000 credit card debt after 2 years if the interest rate is 20% per year with monthly compounding and no payments are made during that time. To calculate the compounded debt, the formula A = P(1 + r/n)^(nt) is used, where A is the amount owed, P is the principal amount ($5,000), r is the annual interest rate (0.20), n is the number of times that interest is compounded per unit t, and t is the time the money is invested for. In this case, with monthly compounding, n is 12 and t is 2 years.

Using the formula, A = $5,000(1 + 0.20/12)^(12*2), which calculates to an amount greater than the original $5,000. It's important to note that making minimum payments or more than the minimum payments can significantly affect the time it takes to pay off a credit card balance, as seen in the various examples provided.

User Matthew Regul
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1 vote

Final answer:

The student will owe approximately $7,444.29 on a $5,000 credit card debt after 2 years without making payments, considering a 20% annual interest rate with monthly compounding.

Step-by-step explanation:

To calculate how much a student will owe on a $5,000 credit card debt with a 20% annual interest rate and monthly compounding after 2 years without making any payments, you can use the formula for compound interest:

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

Where:

  • A is the amount of money accumulated after n years, including interest.
  • P is the principal amount (the initial amount of money).
  • r is the annual interest rate (decimal).
  • n is the number of times that interest is compounded per year.
  • t is the time the money is invested for, in years.

Plugging the values into the formula gives us:

A = $5,000(1 + 0.20/12)^(12*2)

A = $5,000(1 + 0.01667)^(24)

A = $5,000(1.01667)^(24)

A ≈ $5,000(1.488859)

A ≈ $7,444.29

After 2 years, with no payments made, the student will owe approximately $7,444.29 on the original $5,000 credit card debt.

User Sarita
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