Answer:
Part a) [tex]\$6,539.48[/tex]
Part b) [tex]5.36\ years[/tex]
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
Part a) What is the amount after 2 years?
we have
[tex]t=2\ years\\ P=\$5,800\\ r=0.06[/tex]
substitute in the formula above
[tex]A=\$5,800(e)^{0.06*2}=\$6,539.48[/tex]
Part b) How long will it take for the amount to be $8000?
we have
[tex]t=?\ years\\ P=\$5,800\\ r=0.06\\A=\$8,000[/tex]
substitute in the formula above and solve for t
[tex]\$8,000=\$5,800(e)^{0.06t}[/tex]
[tex](8,000/5,800)=(e)^{0.06t}[/tex]
Applying ln both sides
Remember that
ln(e)=1
[tex]ln(8,000/5,800)=0.06t[/tex]
[tex]t=ln(8,000/5,800)/0.06=5.36\ years[/tex]
