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Currently you have two credit cards, h and i. card h has a balance of $1,186.44 and an interest rate of 14.74%, compounded annually. card i has a balance of $1,522.16 and an interest rate of 12.05%, compounded monthly. assuming that you make no purchases and no payments with either card, after three years, which card’s balance will have increased by more, and how much greater will that increase be?

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RileyMyers

Answer:

a. Card I’s balance increased by $53.16 more than Card H’s balance.

Using compound interest, it is found that Card's I balance increased by $53.16 more than Card's H balance.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

  • A(t) is the amount of money after t years.
  • P is the principal(the initial sum of money).
  • r is the interest rate(as a decimal value).
  • n is the number of times that interest is compounded per year.
  • t is the time in years for which the money is invested or borrowed.

For card H, we have that:

[tex]P = 1186.44, r = 0.1474, n = 1, t = 3[/tex].

Hence:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(t) = 1186.44\left(1 + \frac{0.1474}{1}\right)^{3}[/tex]

[tex]A(t) = 1792.22[/tex]

The increase was of:

1792.22 - 1186.44 = $605.78.

For card I, we have that:

[tex]P = 1522.16, r = 0.1205, n = 12, t = 3[/tex].

Hence:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(t) = 1522.16\left(1 + \frac{0.1205}{12}\right)^{36}[/tex]

[tex]A(t) = 2181.10[/tex]

The increase was of:

2181.1 - 1522.16 = $658.94.

The difference of the increases is of:

658.94 - 605.78 = $53.16.

Hence, Card's I balance increased by $53.16 more than Card's H balance.

More can be learned about compound interest at https://brainly.com/question/25781328

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