Given:
Principal amount= $11000
Total amount = $12950
Rate = 5% compunded semi-annually.
The formula for compound interest is,
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt^{}} \\ A=12950,P=11000,r=5\text{ \%},n=2 \\ 12950=11000(1+\frac{5}{2\times100})^{2t} \\ \frac{12950}{11000}=(1+0.025)^{2t} \\ \frac{259}{220}=1.025^{2t} \\ Apply\text{ exponent rule} \\ \ln (\frac{259}{220})=2t\ln (1.025) \\ t=\frac{\ln (\frac{259}{220})}{2\ln (1.025)} \\ t=3.305 \end{gathered}[/tex]Answer: the amount is invested for 3.305 years . It is about 3 years 4 months.
