IDNLearn.com: Your trusted platform for finding precise and reliable answers. Get prompt and accurate answers to your questions from our community of knowledgeable experts.
Sagot :
To determine the balance in the account after 12 years with an initial deposit of [tex]$750, an annual interest rate of 9%, and quarterly compounding, we use the compound interest formula:
\[ F = P \left(1 + \frac{r}{n}\right)^{nt} \]
where:
- \( P \) is the principal amount (initial deposit),
- \( r \) is the annual interest rate,
- \( n \) is the number of times interest is compounded per year,
- \( t \) is the number of years the money is invested.
Let's plug in the given values:
- \( P = 750 \)
- \( r = 0.09 \)
- \( n = 4 \)
- \( t = 12 \)
First, calculate the expression inside the parentheses:
\[ \frac{r}{n} = \frac{0.09}{4} = 0.0225 \]
Next, add 1 to this value:
\[ 1 + \frac{r}{n} = 1 + 0.0225 = 1.0225 \]
Raise this value to the power of \( n \times t \):
\[ n \times t = 4 \times 12 = 48 \]
\[ \left(1.0225\right)^{48} \]
Using the given result, we know that:
\[ \left(1.0225\right)^{48} \approx 2.909639612 \]
Finally, multiply this by the principal \( P = 750 \):
\[ F = 750 \times 2.909639612 \approx 2182.2297090673655 \]
Rounding to the nearest cent, the balance after 12 years is:
\[ F = 2182.23 \]
Thus, the balance after 12 years is \(\$[/tex]2182.23\).
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.