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The outstanding balance on Bill's credit card account is $3200. The bank issuing the credit card charges 9.3% per year compounded monthly. If Bill decides to pay off this balance in equal monthly installments at the end of each month for the next 18 months, how much will his monthly payment be? What is the effective rate of interest the bank is charging Bill?

User Iberbeu
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Answer:

Explanation:

To calculate Bill's monthly payment, we can use the formula for the monthly payment on a loan:

P = (r * PV) / (1 - (1 + r)^(-n))

Where:

  • P = Monthly payment
  • r = Monthly interest rate
  • PV = Present value or outstanding balance
  • n = Number of months

In this case, the outstanding balance is $3200, and the loan term is 18 months. The monthly interest rate can be calculated by dividing the annual interest rate by 12. The annual interest rate is 9.3%.

r = 9.3% / 12 = 0.775% (expressed as a decimal)

Now we can substitute the values into the formula:

P = (0.00775 * 3200) / (1 - (1 + 0.00775)^(-18))

Using a calculator, we can solve for P:

P ≈ $191.47

Therefore, Bill's monthly payment will be approximately $191.47.

To calculate the effective rate of interest the bank is charging Bill, we can use the formula:

Effective Rate = (1 + r/n)^n - 1

Where:

  • r = Annual interest rate
  • n = Number of compounding periods per year

In this case, the annual interest rate is 9.3% and the compounding is monthly, so n = 12.

Substituting the values into the formula:

Effective Rate = (1 + 0.093/12)^12 - 1

Using a calculator, we can solve for the effective rate:

Effective Rate ≈ 9.55%

Therefore, the bank is charging Bill an effective rate of interest of approximately 9.55%.

User Robin Weston
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