Problem

Use the compound-interest formula to find the account balance $A$, where $P$ is principal, $r$ is interest rate, $n$ is number of compounding periods per year, $t$ is time, years, and $\mathrm{A}$ is account balance. \begin{tabular}{|c|c|c|c|} \hline P & r & compounded & $\mathbf{t}$ \\ \hline$\$ 14,585$ & $6.8 \%$ & Daily & 5 \\ \hline \end{tabular} The account balance is approximately $\$ \square$.

Solution

Step 1 :Given the principal amount \(P = \$ 14,585\), the interest rate \(r = 6.8 \% = 0.068\), the number of compounding periods per year \(n = 365\) (daily), and the time \(t = 5\) years, we are asked to find the account balance \(A\).

Step 2 :We use the compound-interest formula: \(A = P \times (1 + \frac{r}{n})^{n \times t}\).

Step 3 :Substituting the given values into the formula, we get: \(A = 14585 \times (1 + \frac{0.068}{365})^{365 \times 5}\).

Step 4 :Calculating the above expression, we find that \(A \approx 20490.51171892015\).

Step 5 :Rounding to the nearest cent, we get the final account balance: \(\boxed{\$20490.51}\).

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