Respuesta :
To solve this question, we need to use the formula of compound interest
[tex]\begin{gathered} A=p(1+\frac{r}{n})^{nt} \\ A=10,230 \\ p=5000 \\ r=5\text{ \%=0.05} \\ n=2 \\ t=\text{ ?} \end{gathered}[/tex]We would have to input these values into the above equation and solve for t
[tex]\begin{gathered} a=p(1+\frac{r}{n})^{nt} \\ 10230=5000(1+\frac{0.05}{2})^{2\times t} \\ \frac{10230}{5000}=(1+0.025)^{2t} \\ 2.046=1.025^{2t} \\ \text{Take the log of both sides} \\ \log 2.046=\log 1.025^{2t^{}} \\ \log 2.046=2t\log 1.025 \\ 2t=\frac{\log 2.046}{\log 1.025} \\ 2t=28.99 \\ \frac{2t}{2}=\frac{28.99}{2} \\ t=14.5 \end{gathered}[/tex]It will take 14 years and 6 months for $5000 compounded annually at 5% to get to $10,230
