IDNLearn.com offers a comprehensive platform for finding and sharing knowledge. Our experts are ready to provide prompt and detailed answers to any questions you may have.
Sagot :
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].
### 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].
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for choosing IDNLearn.com. We’re committed to providing accurate answers, so visit us again soon.
