Question

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?

Answer 1

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:

$A(t) = P(1 + \frac{r}{n})^{nt}$

• 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:

$A(t) = 5 \times 200 \times 12 = 12000$

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

$A(t) = P(1 + \frac{r}{n})^{nt}$

$12000 = P(1 + \frac{0.065}{12})^{60}$

$1.38282P = 12000$

$P = \frac{12000}{1.38282}$

$P = 8678$

To the nearest 100, $8,700.

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

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