QuestionSuppose that $\$ 2000$ is invested at a rate of $5.2 \%$, compounded quarterly. Assuming that no withdrawals are made, find the total amount after 5 years.
Do not round any intermediate computations, and round your answer to the nearest cent.

Studdy Solution
Compute the total amount. First, calculate the expression inside the parentheses:
$$1 + \frac{0.052}{4} = 1 + 0.013 = 1.013$$
Next, calculate the exponent:
$$4 \times 5 = 20$$
Now, raise the base to the power of the exponent:
$$1.013^{20} \approx 1.296856$$
Finally, multiply by the principal amount:
$$A = 2000 \times 1.296856 \approx 2593.71$$
The total amount after 5 years, rounded to the nearest cent, is:
$$\boxed{2593.71}$$