Question 2(Multiple Choice Worth 5 points)
(Types of Interest MC)
A principal amount of $\$ 14,390$ is placed in a savings account with an annual interest rate of $4.13 \%$ compounded monthly. How much interest does the account earn after 21 years?
$\$ 19,814.06$
$\$ 19,86503$
$\$ 34,204.06$
$\$ 34,255.03$

Step 1 ：Given that the principal amount (P) is $14,390, the annual interest rate (r) is 4.13% or 0.0413 in decimal, the number of times that interest is compounded per year (n) is 12, and the time the money is invested for in years (t) is 21.

Step 2 ：We can use the formula for compound interest, which is \(A = P(1 + \frac{r}{n})^{nt}\), where A is the amount of money accumulated after n years, including interest.

Step 3 ：Substituting the given values into the formula, we get \(A = 14390(1 + \frac{0.0413}{12})^{12*21}\).

Step 4 ：Solving the equation, we get \(A = 14390(1.0034416667)^{252}\) and then \(A = 14390(2.4569)\).

Step 5 ：So, the total amount A after 21 years is approximately $35,394.06.

Step 6 ：The interest earned is the total amount A minus the principal P, which is \(Interest = A - P\).

Step 7 ：Substituting the values, we get \(Interest = $35,394.06 - $14,390\).

Step 8 ：\(\boxed{Interest = $21,004.06}\). So, the interest earned after 21 years is approximately $21,004.06.