To find the value of a savings account started with [tex]$2,700, earning 5 percent interest compounded annually after 8 years, we can make use of the compound interest formula. The compound interest formula is given by:
\[ A = P \left(1 + \frac{r}{n}\right)^{n \cdot t} \]
where:
- \( A \) is the amount in the savings account after the specified time.
- \( P \) is the principal amount (initial deposit), which is $[/tex]2,700.
- [tex]\( r \)[/tex] is the annual interest rate (decimal form), which is 0.05 for 5%.
- [tex]\( n \)[/tex] is the number of times the interest is compounded per year. Since the interest is compounded annually, [tex]\( n = 1 \)[/tex].
- [tex]\( t \)[/tex] is the number of years the money is invested, which is 8 years in this case.
Applying these values to the formula:
[tex]\[
A = 2700 \left(1 + \frac{0.05}{1}\right)^{1 \times 8}
\][/tex]
Simplify the expression inside the parentheses:
[tex]\[
A = 2700 \left(1 + 0.05\right)^8
\][/tex]
[tex]\[
A = 2700 \left(1.05\right)^8
\][/tex]
Now, compute [tex]\( (1.05)^8 \)[/tex]. From the training and given the result, we know:
[tex]\( (1.05)^8 \approx 1.477 \)[/tex]
So the equation becomes:
[tex]\[
A = 2700 \times 1.477
\][/tex]
Finally, perform the multiplication:
[tex]\[
A = 3989.13
\][/tex]
Thus, the value of the savings account after 8 years is $3,989.13.
