# 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?

###### Question:

## Answers

Using compound interest, it is found that the maximum amount of money he can borrow is of $8,700.------------------------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.A similar problem is given at https://brainly.com/question/15340331