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Andy is considering taking a loan to remodel his kitchen. He is offered a loan by his bank for five years and an annual interest of 6.5% with monthly payments. To the nearest $100, what is the maximum amount of money he can borrow if he can only afford to pay back $200 per month?

Sagot :

Using compound interest, it is found that the maximum amount of money he can borrow is of $8,700.

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The compound interest formula is given by:

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

  • 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).
  • n is the number of times that interest is compounded per year.
  • t is the time in years.

Maximum monthly payments of $200 per month per five years, thus:

[tex]A(t) = 5 \times 200 \times 12 = 12000[/tex]

  • Interest rate of 6.5%, thus [tex]r = 0.065[/tex].
  • Monthly payments, thus [tex]n = 12[/tex].
  • Five years, thus [tex]t = 5[/tex].
  • The amount he can borrow is the principal.

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

[tex]12000 = P(1 + \frac{0.065}{12})^{60}[/tex]

[tex]1.38282P = 12000[/tex]

[tex]P = \frac{12000}{1.38282}[/tex]

[tex]P = 8678[/tex]

To the nearest 100, $8,700.

The maximum amount of money he can borrow is of $8,700.

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