IDNLearn.com: Your go-to resource for finding expert answers. Discover prompt and accurate responses from our experts, ensuring you get the information you need quickly.
Sagot :
Certainly! Let's go through the compound interest formula step-by-step to determine the balance after 3 years for a deposit of [tex]$500 at an annual interest rate of 4%, compounded annually.
The formula for compound interest is:
\[ V(t) = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( P \) is the initial (principal) investment.
- \( r \) is the annual interest rate (as a decimal).
- \( n \) is the number of times the interest is compounded per year.
- \( t \) is the number of years.
- \( V(t) \) is the value of the investment after \( t \) years.
Given the parameters:
- \( P = 500 \) (the initial deposit),
- \( r = 0.04 \) (4% annual interest rate),
- \( n = 1 \) (compounded annually),
- \( t = 3 \) (3 years),
We can plug these values into the formula:
\[ V(3) = 500 \left(1 + \frac{0.04}{1}\right)^{1 \cdot 3} \]
First, simplify inside the parenthesis:
\[ 1 + \frac{0.04}{1} = 1.04 \]
Now raise \( 1.04 \) to the power of \( 3 \):
\[ 1.04^3 \]
Calculate \( 1.04^3 \):
\[ 1.04^3 = 1.124864 \]
Now multiply this result by the initial principal \( P \):
\[ 500 \times 1.124864 \]
This gives:
\[ 562.432 \]
Rounding to two decimal places (as is standard for currency), we get:
\[ 562.43 \]
Therefore, the balance after 3 years, when the interest is compounded annually, is:
\[ \boxed{562.43} \]
So, based on the given options, the correct answer is:
\[ \$[/tex] 562.43 \]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.