ANSWER:
39.61 years
STEP-BY-STEP EXPLANATION:
Formula for continous compounding is given by:
[tex]A=P\cdot e^{rt}[/tex]Where,
A = Future Amount: Since investement double = $2600*2 = $5200
P = Principal Amount = $2600
r = Rate of interest = 1.75% = 1.75/100 = 0.0175
t = Time in years = t
Replaicng:
[tex]\begin{gathered} 5200=2600\cdot e^{0.0175\cdot t} \\ \frac{5200}{2600}=e^{0.0175\cdot t} \\ e^{0.0175t}=2 \\ 0.0175t=\ln 2 \\ t=\frac{\ln 2}{0.0175} \\ t=39.608\cong39.61\text{ years} \end{gathered}[/tex]After 39.61 years the initial investment will double
