Answer: 9.9 years.
Step-by-step explanation:
If interest is compounded continuously, then formula to compute final amount A = [tex]Pe^{rt}[/tex], where P =initial amount, r= rate of interest , t=time.
Given: P= $61,000, r= 1.9% =0.019 , A = $ 73600
Substitute all values in formula
[tex]73600=61000e^{0.019t}\\\\\Rightarrow\ \dfrac{73600}{61000}=e^{0.019t}\\\\\Rightarrow\ 1.20655738=e^{0.019t}[/tex]
Taking natural log on both sides
[tex]\ln (1.20655738)=0.019t\\\\\\ 0.18777116=0.019t\\\\\\ t=\dfrac{0.18777116}{0.019}\\\\\\ t=9.88269263\approx9.9\ \text{years}[/tex]
Hence, the required time = 9.9 years.
