We have been given that Aubrey invested $7,100 in an account paying an interest rate of 5.6% compounded quarterly. We are asked to find the amount is account after 19 years.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year.
t = Time in years.
[tex]5.6\%=\frac{5.6}{100}=0.056[/tex]
[tex]n=4[/tex], [tex]t=19[/tex] and [tex]P=\$7100[/tex]
[tex]A=\$7,100(1+\frac{0.056}{4})^{4\cdot 19}[/tex]
[tex]A=\$7,100(1+0.014)^{76}[/tex]
[tex]A=\$7,100(1.014)^{76}[/tex]
[tex]A=\$7,100(2.8766338050114077)[/tex]
[tex]A=\$20,424.10001558099467[/tex]
Upon rounding to nearest ten dollars, we will get:
[tex]A\approx \$20,420[/tex]
Therefore, there will be approximately $20,420 in the account after 19 years.
