Sure, let's solve this compound interest problem step by step.
Given:
- Principal amount ([tex]\( P \)[/tex]) = [tex]$7,200
- Annual interest rate (\( r \)) = 2.3% (which is 0.023 in decimal form)
- Number of times the interest is compounded per year (\( n \)) = 4 (quarterly)
- Number of years (\( t \)) = 12
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
1. Substitute the given values into the formula:
\[ A = 7200 \left(1 + \frac{0.023}{4}\right)^{4 \times 12} \]
2. Simplify the expression inside the parentheses:
\[ 1 + \frac{0.023}{4} = 1 + 0.00575 = 1.00575 \]
3. Raise this value to the power of \( 4 \times 12 \):
\[ (1.00575)^{48} \]
4. Multiply the principal amount with the resulting value:
\[ A = 7200 \times (1.00575)^{48} \]
5. Calculate the final amount:
\[ A \approx 9481.007193983489 \]
6. Round the final amount to the nearest dollar:
\[ A \approx 9481 \]
So, after 12 years, Dylan would have approximately $[/tex]9,481 in the account.
