Answer:
6.93 years.
Step-by-step explanation:
We have been given that $3550 is invested at 10.0% compounded continuously.
To solve our given problem, we will use continuous compounding formula.
[tex]A=P\cdot e^{rt}[/tex], where,
A = Final amount,
P = Principal amount,
e = Mathematical constant,
r = Interest rate in decimal form,
t = Time
[tex]10\%=\frac{10}{100}=0.10[/tex]
Substitute the given values:
[tex]7100=3550\cdot e^{0.10t}[/tex]
[tex]\frac{7100}{3550}=\frac{3550\cdot e^{0.10t}}{3550}[/tex]
[tex]2=e^{0.10t}[/tex]
Take natural log of both sides:
[tex]\text{ln}(2)=\text{ln}(e^{0.10t})[/tex]
Using property [tex]\text{ln}(a^b)=b\cdot \text{ln}(a)[/tex], we will get:
[tex]\text{ln}(2)=0.10t\cdot \text{ln}(e)[/tex]
[tex]0.6931471805599453=0.10t\cdot 1[/tex]
[tex]0.6931471805599453=0.10t[/tex]
Switch sides:
[tex]0.10t=0.6931471805599453[/tex]
[tex]\frac{0.10t}{0.10}=\frac{0.6931471805599453}{0.10}[/tex]
[tex]t=6.9314718[/tex]
[tex]t\approx 6.93[/tex]
Therefore, it will take approximately 6.93 years for the balance to reach $7100.
