Respuesta :

JcAlmighty
The answer is 0.02

A = P(1 + r/n)ⁿˣ
A - the final amount
P - the principal (the initial amount)
r - the annual interest rate
n - the number of times that interest is compounded per year
x - the number of years

We have:
A = $572.60
P = $560.00
r = ?
n = 2
x = 1

572.60 = 560 * (1 + r/2)²*¹
572.60 = 560 * (1 + r/2)²
572.60 : 560 = (1 + r/2)²
572.60 = 1² + 2 * 1 * r/2 + (r/2)²
1.0225 = 1 + r + r²/4
4 * 1.0225 = 4 * 1 + 4 * r + 4 * r²/4
4.09 = 4 + 4r + r²
0 = 4 + 4r + r² - 4.09
0 = r² + 4r - 0.09
r² + 4r - 0.09 = 0

[tex]r _{1,2} = \frac{-4+/- \sqrt{4^{2} -4*1*(-0.09)} }{2*1} = \frac{-4+/- \sqrt{16+0.36} }{2}= \frac{-4+/- \sqrt{16.36} }{2}= \\ \\ = \frac{-4+/-4.04}{2} \\ \\ r_1 = \frac{-4-4.04}{2} =-4.02 \\ \\ r_2 = \frac{-4+4.04}{2} =-0.02[/tex]

The rate cannot be negative, so it is 0.02

Otras preguntas