Answer:
a. $1251.5
b. $1254.64
c. 15.4 years
d. 30.56 years
Step-by-step explanation:
Given the information:
As we know, the formula to find the future value of Jackie deposit with interest is compounded monthly, quaterly, ..is
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex] where:
Hence:
a. If the interest is compounded quarterly how much money will Jackie have in 10 years?
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
<=> [tex]A=800(1+\frac{0.045}{4} )^{4*10}[/tex]
<=> A = $1251.5
d. If Jackie's money is compounded monthly, how long will it take her money to triple?
<=> [tex]A=P(1+\frac{r}{n} )^{nt} = 3*800[/tex]
<=> [tex]800(1+\frac{0.045}{12} )^{12*t} = 2400[/tex]
<=> [tex](1+\frac{0.045}{12} )^{12*t} = 3[/tex]
<=> t = 30.56 years
As we know, the formula to find the future value of Jackie deposit with interest is compounded continuously
A = P*[tex]e^{rt}[/tex] where e is the mathematical constant approximated as 2.7183.
b. If the interest is compounded continuously how much money will Jackie have in 10 years?
<=> A = 800*[tex]2.7183^{0.045*10}[/tex]
<=> A = $1254.64
C. If Jackie's money is compounded continuously, how long will it take her money to double?
<=> P*[tex]e^{rt}[/tex] = 2*800
<=> 800*[tex]2.7183^{0.045*t}[/tex] = 1600
<=> [tex]2.7183^{0.045*t}[/tex] = 2
<=> t = 15.4 years
