Answer:
The earning rate is approximately 0.08.
Step-by-step explanation:
We can determine the yearly rate by means of compound interest, which is defined by:
[tex]C(t) = C_{o}\cdot (1+r)^{t}[/tex] (Eq. 1)
Where:
[tex]C_{o}[/tex] - Initial deposit, measured in US dollars.
[tex]r[/tex] - Earning rate, dimensionless.
[tex]t[/tex] - Earning periods, measured in years.
We proceed to clear the earning rate within:
[tex]\frac{C(t)}{C_{o}} = (1+r)^{t}[/tex]
[tex]\log \frac{C(t)}{C_{o}} = t\cdot \log (1+r)[/tex]
[tex]\frac{1}{t}\cdot \log \frac{C(t)}{C_{o}} = \log (1+r)[/tex]
[tex]\log \left(\frac{C(t)}{C_{o}} \right)^{\frac{1}{t} } = \log (1+r)[/tex]
[tex]\left(\frac{C(t)}{C_{o}} \right)^{\frac{1}{t} } = 1+r[/tex]
[tex]r = \left(\frac{C(t)}{C_{o}} \right)^{\frac{1}{t} }-1[/tex]
If we know that [tex]C(9) = 2\cdot C_{o}[/tex] and [tex]t = 9[/tex], then the earning rate is:
[tex]r = 2^{\frac{1}{9} }-1[/tex]
[tex]r \approx 0.08[/tex]
The earning rate is approximately 0.08.
