Certainly! Let's go through this step-by-step to determine the final value of the investment after two years, with an annual compounding interest rate of 8%, and round our answers to the nearest cent.
### Initial Investment
- Principal: [tex]\( \$ 650 \)[/tex]
### First Year
1. Calculate the Interest Earned in the First Year:
- Interest Rate: 8%
- Interest Earned = Principal [tex]\(\times\)[/tex] Interest Rate
[tex]\[
\text{Interest Earned} = 650 \times 0.08 = 52.00
\][/tex]
2. Calculate the Total at the End of the First Year:
- Total = Principal [tex]\(\+\)[/tex] Interest Earned
[tex]\[
\text{First Year Total} = 650 + 52.00 = 702.00
\][/tex]
### Second Year
1. Calculate the Interest Earned in the Second Year:
- New Principal = First Year Total = [tex]\( \$ 702 \)[/tex]
- Interest Earned = New Principal [tex]\(\times\)[/tex] Interest Rate
[tex]\[
\text{Interest Earned} = 702.00 \times 0.08 = 56.16
\][/tex]
2. Calculate the Total at the End of the Second Year:
- Total = New Principal [tex]\(\+\)[/tex] Interest Earned
[tex]\[
\text{Second Year Total} = 702.00 + 56.16 = 758.16
\][/tex]
### Summary
Let's populate our table now:
| Year | Principal | Interest Earned | Total |
|--------------|-------------|-----------------|-------------|
| First Year | \[tex]$650 | \$[/tex]52.00 | \[tex]$702.00 |
| Second Year | \$[/tex]702.00 | \[tex]$56.16 | \$[/tex]758.16 |
In more detail:
1. First Year:
- Principal: [tex]\( \$ 650 \)[/tex]
- Interest Earned: [tex]\( \$ 52.00 \)[/tex]
- Total: [tex]\( \$ 702.00 \)[/tex]
2. Second Year:
- Principal: [tex]\( \$ 702.00 \)[/tex] (which is the total from the end of the first year)
- Interest Earned: [tex]\( \$ 56.16 \)[/tex]
- Total: [tex]\( \$ 758.16 \)[/tex]
### Filling in the Table
Given the question prompts:
- First Year:
[tex]\[
\text{Principal}: \$ 650 \text{, Interest Earned: } \$ 52.00 \text{, Total: } \$ 702.00
\][/tex]
- Second Year:
- [tex]$ \text{Principal at start of the second year: } \$[/tex] 702.00 [tex]$
\[
\text{Interest Earned: } \$[/tex] 56.16
\]
[tex]\[
\text{Total at the end of the second year: } \$ 758.16
\][/tex]
Thus, the completed table will be:
| Year | Principal | Interest Earned | Total |
|--------------|-------------|------------------|--------------|
| First Year | \[tex]$650 | \$[/tex]52.00 | \[tex]$702.00 |
| Second Year | \$[/tex]702.00 | \[tex]$56.16 | \$[/tex]758.16 |
And the final value of the investment after two years is: [tex]\( \$ 758.16 \)[/tex].
