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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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