Respuesta :
Given:
Principal value = $2300
Rate of interest = 14% compounded continuously.
To find:
The time taken by Brad's investment to triple.
Solution:
The formula for amount after the compound interest (Continuously) is:
[tex]A=Pe^{rt}[/tex]
Where, P is the principal, r is the rate of interest in decimal and t is the time period.
Triple of Brad's investment is
[tex]3\times \$ 2300=\$ 6900[/tex]
Substituting [tex]A=6900,P=2300\ r=0.14[/tex], we get
[tex]6900=2300e^{0.14t}[/tex]
[tex]\dfrac{6900}{2300}=e^{0.14t}[/tex]
[tex]3=e^{0.14t}[/tex]
Taking natural log on both sides, we get
[tex]\ln 3=\ln e^{0.14t}[/tex]
[tex]1.0986=0.14t[/tex] [tex][\because \ln e^x=x][/tex]
[tex]\dfrac{1.0986}{0.14}=t[/tex]
[tex]7.84714=t[/tex]
After approximating the value, we get
[tex]t\approx 7.85[/tex]
Therefore, Brad's investment will take 7.85 years to triple.
