Respuesta :
Using compound interest equations, it is found that Lauren will have $626 more in her account.
Compound interest:
The equation for compound interest is:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
- A(t) is the amount of money after t years.
- P is the principal(the initial sum of money).
- r is the interest rate(as a decimal value).
- n is the number of times that interest is compounded per year.
- t is the time in years for which the money is invested or borrowed.
Considering continuous compounding, the equation is:
[tex]A(t) = Pe^{rt}[/tex]
For Lauren, we have that:
- Continuous compounding with a rate of [tex]7\frac{5}{8}\%[/tex], hence [tex]r = 0.07625[/tex]
The time it takes to triple is t for which A(t) = 3P, hence:
[tex]A(t) = Pe^{rt}[/tex]
[tex]3P = Pe^{0.07625t}[/tex]
[tex]e^{0.07625t} = 3[/tex]
[tex]\ln{e^{0.07625t}} = \ln{3}[/tex]
[tex]0.07625t = \ln{3}[/tex]
[tex]t = \frac{\ln{3}}{0.07625}[/tex]
[tex]t = 14.4[/tex]
For Adrian, we have that:
- Invested $9,600, hence [tex]P = 9600[/tex].
- Interest rate of [tex]7\frac{1}{2}\%[/tex], hence [tex]r = 0.075[/tex].
- Compounded monthly, hence [tex]n = 12[/tex].
In 14.4 years, he will have:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(14.4) = 9600\left(1 + \frac{0.075}{12}\right)^{12(14.4)}[/tex]
[tex]A(14.4) = 28174[/tex]
Lauren's amount is of 3 x 9600 = 28800.
28800 - 28174 = 626.
Lauren will have $626 more in her account.
To learn more about compound interest equations, you can take a look at https://brainly.com/question/25537936
