Problem
The principal represents an amount of money deposited in a savings account subject to compound interest at the given rate. \begin{tabular}{|c|c|c|c|} \hline Principal & Rate & Compounded & Time \\ \hline$\$ 5000$ & $3 \%$ & semiannually & 5 years \\ \hline \end{tabular} A. Find how much money there will be in the account after the given number of years. B. Find the interest earned. (i) Click the icon to view some finance formulas. A. The amount of money in the account after 5 years is $\$ \square$. (Round to the nearest hundredth as needed.)
Solution
Step 1 ：Given the principal amount (P) is $5000, the annual interest rate (r) is 3% or 0.03 in decimal, the interest is compounded semiannually (n = 2), and the time (t) is 5 years.
Step 2 ：We use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest.
Step 3 ：Substitute the given values into the formula: A = 5000(1 + 0.03/2)^(2*5)
Step 4 ：Solving the equation gives A = 5802.704125125745
Step 5 ：Rounding to the nearest hundredth, the amount of money in the account after 5 years is \(\boxed{\$5802.70}\)
