Answer :
To complete the table and understand how the investment grows with monthly compounding interest, let’s go through the process of calculating each month's starting balance, interest, and ending balance.
Concept Recap:
When you invest with compound interest, the interest earned each month is added to the principal, or starting balance, for the next month. In this case, you have a 1% monthly interest rate on the initial amount.
Month-by-Month Breakdown:
1. Month 1:
- Starting Balance: \[tex]$3700.00
- Interest: 1% of \$[/tex]3700 is \[tex]$37.00
- Ending Balance: \$[/tex]3700 + \[tex]$37 = \$[/tex]3737.00
2. Month 2:
- Starting Balance: \[tex]$3737.00
- Interest: 1% of \$[/tex]3737 is \[tex]$37.37 (rounded to two decimal places)
- Ending Balance: \$[/tex]3737 + \[tex]$37.37 = \$[/tex]3774.37
3. Month 3:
- Starting Balance: \[tex]$3774.37
- Interest: 1% of \$[/tex]3774.37 is \[tex]$37.74 (rounded to two decimal places)
- Ending Balance: \$[/tex]3774.37 + \[tex]$37.74 = \$[/tex]3812.11
4. Month 4:
- Starting Balance: \[tex]$3812.11
- Interest: 1% of \$[/tex]3812.11 is \[tex]$38.12 (rounded to two decimal places)
- Ending Balance: \$[/tex]3812.11 + \[tex]$38.12 = \$[/tex]3850.23
5. Month 5:
- Starting Balance: \[tex]$3850.23
- Interest: 1% of \$[/tex]3850.23 is \[tex]$38.50
- Ending Balance: \$[/tex]3850.23 + \[tex]$38.50 = \$[/tex]3888.73
Using these steps, you can accurately track how your investment grows each month with the given conditions. Each month's interest is based on the previous month's ending balance, reinforcing the concept of compound interest.
Concept Recap:
When you invest with compound interest, the interest earned each month is added to the principal, or starting balance, for the next month. In this case, you have a 1% monthly interest rate on the initial amount.
Month-by-Month Breakdown:
1. Month 1:
- Starting Balance: \[tex]$3700.00
- Interest: 1% of \$[/tex]3700 is \[tex]$37.00
- Ending Balance: \$[/tex]3700 + \[tex]$37 = \$[/tex]3737.00
2. Month 2:
- Starting Balance: \[tex]$3737.00
- Interest: 1% of \$[/tex]3737 is \[tex]$37.37 (rounded to two decimal places)
- Ending Balance: \$[/tex]3737 + \[tex]$37.37 = \$[/tex]3774.37
3. Month 3:
- Starting Balance: \[tex]$3774.37
- Interest: 1% of \$[/tex]3774.37 is \[tex]$37.74 (rounded to two decimal places)
- Ending Balance: \$[/tex]3774.37 + \[tex]$37.74 = \$[/tex]3812.11
4. Month 4:
- Starting Balance: \[tex]$3812.11
- Interest: 1% of \$[/tex]3812.11 is \[tex]$38.12 (rounded to two decimal places)
- Ending Balance: \$[/tex]3812.11 + \[tex]$38.12 = \$[/tex]3850.23
5. Month 5:
- Starting Balance: \[tex]$3850.23
- Interest: 1% of \$[/tex]3850.23 is \[tex]$38.50
- Ending Balance: \$[/tex]3850.23 + \[tex]$38.50 = \$[/tex]3888.73
Using these steps, you can accurately track how your investment grows each month with the given conditions. Each month's interest is based on the previous month's ending balance, reinforcing the concept of compound interest.
