Answer :
Let's analyze the information in the table to determine which statements about Rick and Julian's balances are true:
1. Rick's balance in Year 10 is \[tex]$265.00. - According to the table, Rick's balance in Year 10 is indeed \$[/tex]265.00. This statement is true.
2. Julian's balance in Year 10 is \[tex]$268.78. - According to the table, Julian's balance in Year 10 is indeed \$[/tex]268.78. This statement is true.
3. Rick's balance grows by the same amount each year.
- Rick's interest is calculated using simple interest, which means his balance grows by a fixed amount each year. The yearly increase is: [tex]\(\$200 \times 3.25\% = \$6.50\)[/tex]. This statement is true.
4. Julian's balance grows by the same amount each year.
- Julian's interest is compounded annually, so his balance grows by a different amount each year due to the interest being calculated on the new balance. This statement is false.
5. Julian's balance is always higher than Rick's balance.
- In the early years, Rick's balance is higher than Julian's, but over time, Julian's compounding interest allows his balance to surpass Rick's balance. For example, in Years 1 to 6, Rick's balance is higher, but from Year 7 onwards, Julian's balance is higher. This statement is false.
6. Rick's balance reaches \[tex]$239.00 by Year 6. - According to the table, Rick's balance in Year 6 is \$[/tex]239.00. This statement is true.
7. Julian's balance reaches \[tex]$245.97 by Year 6. - According to the table, Julian's balance in Year 6 is \$[/tex]238.81, not \[tex]$245.97. By Year 7, Julian's balance is \$[/tex]245.97. This statement is false.
8. Julian's balance exceeds \[tex]$250.00 by Year 8. - According to the table, Julian's balance in Year 8 is \$[/tex]253.35. This statement is true.
So, the true statements are:
1. Rick's balance in Year 10 is \[tex]$265.00. 2. Julian's balance in Year 10 is \$[/tex]268.78.
3. Rick's balance grows by the same amount each year.
4. Julian's balance exceeds \$250.00 by Year 8.
1. Rick's balance in Year 10 is \[tex]$265.00. - According to the table, Rick's balance in Year 10 is indeed \$[/tex]265.00. This statement is true.
2. Julian's balance in Year 10 is \[tex]$268.78. - According to the table, Julian's balance in Year 10 is indeed \$[/tex]268.78. This statement is true.
3. Rick's balance grows by the same amount each year.
- Rick's interest is calculated using simple interest, which means his balance grows by a fixed amount each year. The yearly increase is: [tex]\(\$200 \times 3.25\% = \$6.50\)[/tex]. This statement is true.
4. Julian's balance grows by the same amount each year.
- Julian's interest is compounded annually, so his balance grows by a different amount each year due to the interest being calculated on the new balance. This statement is false.
5. Julian's balance is always higher than Rick's balance.
- In the early years, Rick's balance is higher than Julian's, but over time, Julian's compounding interest allows his balance to surpass Rick's balance. For example, in Years 1 to 6, Rick's balance is higher, but from Year 7 onwards, Julian's balance is higher. This statement is false.
6. Rick's balance reaches \[tex]$239.00 by Year 6. - According to the table, Rick's balance in Year 6 is \$[/tex]239.00. This statement is true.
7. Julian's balance reaches \[tex]$245.97 by Year 6. - According to the table, Julian's balance in Year 6 is \$[/tex]238.81, not \[tex]$245.97. By Year 7, Julian's balance is \$[/tex]245.97. This statement is false.
8. Julian's balance exceeds \[tex]$250.00 by Year 8. - According to the table, Julian's balance in Year 8 is \$[/tex]253.35. This statement is true.
So, the true statements are:
1. Rick's balance in Year 10 is \[tex]$265.00. 2. Julian's balance in Year 10 is \$[/tex]268.78.
3. Rick's balance grows by the same amount each year.
4. Julian's balance exceeds \$250.00 by Year 8.
