Find the total amount a college student has in a savings account if $\$ 2,000$ was invested and earned $4 \%$ compounded quarterly for 8 years. Use $A=P\left(1+\frac{r}{n}\right)^{n t}$
The amount after 8 years will be $\$$
(Do not round until the final answer. Then round to the nearest cent as needed.)
Answer
Rounding to the nearest cent, the total amount a college student has in a savings account after 8 years is approximately \(\boxed{2749.88}\).
Step 1 ：Given that the initial amount of money (P) is $2000, the annual interest rate (r) is 4% or 0.04 in decimal form, the number of times that interest is compounded per year (n) is 4 (since it's compounded quarterly), and the time the money is invested for (t) is 8 years.
Step 2 ：We can substitute these values into the compound interest formula, which is \(A=P\left(1+\frac{r}{n}\right)^{n t}\).
Step 3 ：Substituting the given values, we get \(A=2000\left(1+\frac{0.04}{4}\right)^{4 \times 8}\).
Step 4 ：Solving the equation, we find that \(A\approx 2749.8813570621946\).
Step 5 ：Rounding to the nearest cent, the total amount a college student has in a savings account after 8 years is approximately \(\boxed{2749.88}\).
