To determine the ending balance after 8 years of earning 3% interest per year on an initial balance of [tex]$150, we can follow these steps:
1. Understand the Problem: We start with an initial balance of $[/tex]150 and the account earns 3% interest per year for 8 years. We need to find the ending balance after 8 years.
2. Identify the Compound Interest Formula: The formula for compound interest is:
[tex]\[
E = P \times (1 + r)^t
\][/tex]
where:
- [tex]\( E \)[/tex] is the ending balance.
- [tex]\( P \)[/tex] is the initial principal (initial balance).
- [tex]\( r \)[/tex] is the annual interest rate (expressed as a decimal).
- [tex]\( t \)[/tex] is the time the money is invested or borrowed for, in years.
3. Plug in the Given Values: Here, the initial balance [tex]\( P \)[/tex] is [tex]$150, the annual interest rate \( r \) is 3% which is 0.03 in decimal form, and the time \( t \) is 8 years.
\[
E = 150 \times (1 + 0.03)^{8}
\]
4. Simplify Inside the Parenthesis:
\[
1 + 0.03 = 1.03
\]
5. Raise to the Power of 8:
\[
E = 150 \times (1.03)^{8}
\]
6. Calculate the Power:
\[
(1.03)^{8} \approx 1.296136
\]
7. Multiply by the Initial Balance:
\[
E \approx 150 \times 1.296136
\]
\[
E \approx 194.4204
\]
8. Round to the Nearest Cent: The ending balance to the nearest cent is:
\[
E \approx 190.02
\]
So, the ending balance after 8 years is approximately $[/tex]190.02.
