Answer:
The time is about 14 years
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
Let
x ------> the amount of money to be invested
2x ----> the final Investment Value
we have
[tex]t=?\ years\\ P=\$x\\ r=0.05\\A=\$2x[/tex]
substitute in the formula above and solve for t
[tex]2x=x(e)^{0.05t}[/tex]
Simplify
[tex]2=(e)^{0.05t}[/tex]
Apply ln both sides
[tex]ln(2)=(0.05t)ln(e)[/tex]
Remember that
[tex]ln(e)=1[/tex]
[tex]t=ln(2)/(0.05)[/tex]
[tex]t=13.9\ years[/tex]
The doubling time of an investment earning 5% interest if interest is compounded continuously is 13.9 years.
The doubling time of an investment is used to determine when the value of an investment would be double its value currently. When an investment is compounded continously, it means that the investment increases in value constantly over a period of time.
Doubling time = IN 2 / interest rate
(In 2) 0.05 = 13.9 years
To learn more about doubling time, please check: : https://brainly.com/question/21841217
