Question

$\frac{583.2}{500} = ( \frac{100 + r}{100} ) ^{2}$
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Answer 1

I hope that this answer helps you

Answer 2

$\frac{582.2}{500} = ( \frac{100 + r}{100} ) ^{2} \\ = > \frac{582.2}{500} = \frac{(100 + r) ^{2} }{10000} \\ = > 582.2 \times 20 = (100)^{2} + {r}^{2} + 200r \\ = > 11644 = 10000 + {r}^{2} + 200r \\ = > {r}^{2} + 200r - 1644 = 0 \\ = > {r}^{2} + 208r - 8r - 1644 = 0 \\ = > r(r + 208) - 8(r + 208) = 0 \\ = > (r - 8)(r + 208) = 0 \\ = > r = 8 \: or \: r = - 208$

Since ,Rate can't be negative

Therefore Rate of interest is

8%