Answer:
Step-by-step explanation:
Exponential function representing final amount with compound interest compounded continuously,
[tex]A=Pe^{rt}[/tex]
Here, A = Final amount
P = principal amount
r = Rate of interest
t = Duration of investment
For P = $9600
r = 6%
A = 2 × 9600 = $19200
By substituting these values in the formula,
[tex]19200=9600(e)^{0.06\times t}[/tex]
[tex]2=e^{0.06t}[/tex]
[tex]ln(2)=ln(e^{0.06t})[/tex]
ln(2) = 0.06t
t = [tex]\frac{0.693147}{0.06}[/tex]
t = 11.55245
t ≈ 11.5525 years
Any amount will get doubled (with the same rate of interest and duration of investment) in the same time.
Therefore, $960000 will get doubled in 11.5525 years.
