Answer:
Step-by-step explanation:
The key here is to find out how long it will take Justin to triple his money, and then use that number of years in Hailey's equation. If Justin starts with $940, he will triple his money when he has $2820 (940*3). We need to find out how long it takes him to do this using the equation
[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]where A(t) is the tripled amount of money, P is the initial investment, r is the interest rate in decimal form, n is the number of compoundings done per year, and t is the time in years. Filling in and solving for t:
[tex]2820=940(1+\frac{.07625}{12})^{12t[/tex] which simplifies a bit to
[tex]2820=940(1+.0063541667)^{12t[/tex] and a bit more to
[tex]2820=940(1.0063541667)^{12t[/tex] Begin to solve for t by dividing both sides by 940 to get:
[tex]3=(1.0063541667)^{12t[/tex] and then take the natural log of both sides to get the t alone eventually. Taking the natural log on the right side enables us to move the 12t down in front. So doing all of that at the same time:
[tex]ln3=12tln1.0063541667[/tex] and divide both sides by ln(1.0063541667):
[tex]173.4450855=12t[/tex] then finally divide both sides by 12 to get
t = 14.5 years. Now we use that number of years to find out how much Hailey will have.
[tex]A(t)=940(1+\frac{.0825}{4})^{(4)(14.5)}[/tex] which simplifies a bit to
[tex]A(t)=940(1+.020625)^{58[/tex] and a bit more to
[tex]A(t)=940(1.020625)^{58[/tex] and
A(t) = 940(3.26768151) so in 14.5 years, Hailey will have
A(t) = $3071.62
