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jeanine owes $1200 on a credit card. The card charges 16% interest, compounded monthly. Write a formula that describes how much Jeanine will owe on her card after t years, assuming she makes no payments and does not incur any additional charges.

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Edufirst

Answer:

    [tex]P=\$ 12,000\bigg(1+\dfrac{0.16}{12}\bigg)^{(12 t)}[/tex]

Explanation:

To work with monthly compounded interest, you must divide the annual percentage interes rate by 12, to find the monthly percentage interest rate, and multyply the number of years by 12, to find the number of periods.

The fomula is:

         [tex]P=A\bigg(1+\dfrac{r}{n}\bigg)^{(n\times t)}[/tex]

Where:

  • P is the amount owed after t years
  • A is the original debt ($1,200)
  • r is the annual percentage rate: 16% = 0.16
  • n is the number of periods in one year: 12 months
  • t is the number of years

Substituting:

         [tex]P=\$ 12,000\bigg(1+\dfrac{0.16}{12}\bigg)^{(12 t)}[/tex]

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