Answer:
9.15 years
Step-by-step explanation:
step 1
Paisley
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
we have
[tex]t=?\ years\\ P=\$3,000\\ r=0.03\\A=\$9,000[/tex]
substitute in the formula above
[tex]9,000=3,000(e)^{0.03t}[/tex]
solve for t
[tex]3=(e)^{0.03t}[/tex]
apply ln both sides
[tex]ln(3)=ln(e)^{0.03t}[/tex]
[tex]ln(3)=(0.03t)ln(e)[/tex]
[tex]ln(3)=(0.03t)[/tex]
solve for t
[tex]t=ln(3)/(0.03)[/tex]
[tex]t=36.62\ years[/tex]
step 2
Maya
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/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
n is the number of times interest is compounded per year
in this problem we have
[tex]t=?\ years\\ P=\$3,000\\ r=0.04\\A=\$9,000\\n=365[/tex]
substitute in the formula above
[tex]9,000=3,000(1+\frac{0.04}{365})^{365t}[/tex]
solve for t
[tex]3=(\frac{365.04}{365})^{365t}[/tex]
Apply log both sides
[tex]log(3)=log(\frac{365.04}{365})^{365t}[/tex]
[tex]log(3)=(365t)log(\frac{365.04}{365})[/tex]
[tex]t=log(3)/[(365)log(\frac{365.04}{365})][/tex]
[tex]t=27.47\ years[/tex]
step 3
we know that
To find out how much longer would it take for Paisley's money to triple than for Maya's money to triple find the difference in years
[tex]36.62-27.47=9.15\ years[/tex]
