Let's begin by listing out the given information:
Amount after 10 years = $2,100
Time to double = 11 years; A = 2P
The formula for compound interest is given by:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ After\text{ 10 year}s\text{, we have:} \\ A=2,100,n=1(annually),t=10 \\ 2100=P\mleft(1+\frac{r}{1}\mright)^{1\cdot10} \\ 2100=P(1+r)^{10}-----1 \\ \\ After\text{ 11 year}s\text{, we have:} \\ A=2P,n=1,t=11 \\ 2P=P(1+\frac{r}{n})^{1\cdot11} \\ 2P=P(1+\frac{r}{1})^{11} \\ 2P=P(1+r)^{11} \\ \text{Divide both sides by }P\text{:} \\ \frac{2P}{P}=\frac{P(1+r)^{11}}{P} \\ 2=(1+r)^{11}----2 \\ (1+r)=\sqrt[11]{2} \\ 1+r=1.065 \\ r=1.065-1=0.065 \\ r=0.065=6.5\text{ \%} \\ r=6.5\text{ \%} \\ \\ Substitute\text{ the value of r into equation 1, we have:} \\ 2100=P(1+r)^{10} \\ 2100=P(1+0.065)^{10} \\ P(1+0.065)=\sqrt[10]{2100}\Rightarrow P(1.065)=\sqrt[10]{2100}\Rightarrow P=\frac{\sqrt[10]{2100}}{1.065} \\ P=2.018 \end{gathered}[/tex]
