At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Let's complete the table step-by-step by calculating Suzanne's and Derek's annual interest and balance over a 5-year period:
### Suzanne's Investment (Simple Interest)
Suzanne deposits \$7500 in an account earning simple interest at an annual rate of 8%.
1. Calculating Annual Interest:
- The annual interest for Suzanne is calculated as:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} = 7500 \times 0.08 = 600 \][/tex]
2. Calculating Balance for Each Year:
- Year 1:
[tex]\[ \text{Balance}_1 = \text{Principal} + \text{Interest} \times 1 = 7500 + 600 \times 1 = 8100 \][/tex]
- Year 2:
[tex]\[ \text{Balance}_2 = \text{Principal} + \text{Interest} \times 2 = 7500 + 600 \times 2 = 8700 \][/tex]
- Year 3:
[tex]\[ \text{Balance}_3 = \text{Principal} + \text{Interest} \times 3 = 7500 + 600 \times 3 = 9300 \][/tex]
- Year 4:
[tex]\[ \text{Balance}_4 = \text{Principal} + \text{Interest} \times 4 = 7500 + 600 \times 4 = 9900 \][/tex]
- Year 5:
[tex]\[ \text{Balance}_5 = \text{Principal} + \text{Interest} \times 5 = 7500 + 600 \times 5 = 10500 \][/tex]
### Derek's Investment (Compound Interest)
Derek deposits \$7500 in an account earning compound interest at an annual rate of 8%, compounded annually.
1. Calculating Annual Interest and Balance for Each Year:
- Year 0 (Initial Principal):
[tex]\[ \text{Balance}_0 = 7500 \][/tex]
- Year 1:
[tex]\[ \text{Interest}_1 = 7500 \times 0.08 = 600 \][/tex]
[tex]\[ \text{Balance}_1 = 7500 + 600 = 8100 \][/tex]
- Year 2:
[tex]\[ \text{Interest}_2 = 8100 \times 0.08 = 648 \][/tex]
[tex]\[ \text{Balance}_2 = 8100 + 648 = 8748 \][/tex]
- Year 3:
[tex]\[ \text{Interest}_3 = 8748 \times 0.08 = 699.84 \][/tex]
[tex]\[ \text{Balance}_3 = 8748 + 699.84 = 9447.84 \][/tex]
- Year 4:
[tex]\[ \text{Interest}_4 = 9447.84 \times 0.08 = 755.8272 \][/tex]
[tex]\[ \text{Balance}_4 = 9447.84 + 755.8272 = 10203.6672 \][/tex]
- Year 5:
[tex]\[ \text{Interest}_5 = 10203.6672 \times 0.08 = 816.293376 \][/tex]
[tex]\[ \text{Balance}_5 = 10203.6672 + 816.293376 = 11019.960576 \][/tex]
Here's the completed table:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Year} & \begin{array}{c} \text{Suzanne's} \\ \text{Annual} \\ \text{Interest} \end{array} & \begin{array}{c} \text{Suzanne's} \\ \text{Balance} \end{array} & \begin{array}{c} \text{Derek's} \\ \text{Annual} \\ \text{Interest} \end{array} & \begin{array}{c} \text{Derek's} \\ \text{Balance} \end{array} \\ \hline 1 & 600.0 & 8100.0 & 600.0 & 8100.0 \\ 2 & 600.0 & 8700.0 & 648.0 & 8748.0 \\ 3 & 600.0 & 9300.0 & 699.84 & 9447.84 \\ 4 & 600.0 & 9900.0 & 755.8272 & 10203.6672 \\ 5 & 600.0 & 10500.0 & 816.293376 & 11019.960576 \\ \hline \end{array} \][/tex]
### Suzanne's Investment (Simple Interest)
Suzanne deposits \$7500 in an account earning simple interest at an annual rate of 8%.
1. Calculating Annual Interest:
- The annual interest for Suzanne is calculated as:
[tex]\[ \text{Interest} = \text{Principal} \times \text{Rate} = 7500 \times 0.08 = 600 \][/tex]
2. Calculating Balance for Each Year:
- Year 1:
[tex]\[ \text{Balance}_1 = \text{Principal} + \text{Interest} \times 1 = 7500 + 600 \times 1 = 8100 \][/tex]
- Year 2:
[tex]\[ \text{Balance}_2 = \text{Principal} + \text{Interest} \times 2 = 7500 + 600 \times 2 = 8700 \][/tex]
- Year 3:
[tex]\[ \text{Balance}_3 = \text{Principal} + \text{Interest} \times 3 = 7500 + 600 \times 3 = 9300 \][/tex]
- Year 4:
[tex]\[ \text{Balance}_4 = \text{Principal} + \text{Interest} \times 4 = 7500 + 600 \times 4 = 9900 \][/tex]
- Year 5:
[tex]\[ \text{Balance}_5 = \text{Principal} + \text{Interest} \times 5 = 7500 + 600 \times 5 = 10500 \][/tex]
### Derek's Investment (Compound Interest)
Derek deposits \$7500 in an account earning compound interest at an annual rate of 8%, compounded annually.
1. Calculating Annual Interest and Balance for Each Year:
- Year 0 (Initial Principal):
[tex]\[ \text{Balance}_0 = 7500 \][/tex]
- Year 1:
[tex]\[ \text{Interest}_1 = 7500 \times 0.08 = 600 \][/tex]
[tex]\[ \text{Balance}_1 = 7500 + 600 = 8100 \][/tex]
- Year 2:
[tex]\[ \text{Interest}_2 = 8100 \times 0.08 = 648 \][/tex]
[tex]\[ \text{Balance}_2 = 8100 + 648 = 8748 \][/tex]
- Year 3:
[tex]\[ \text{Interest}_3 = 8748 \times 0.08 = 699.84 \][/tex]
[tex]\[ \text{Balance}_3 = 8748 + 699.84 = 9447.84 \][/tex]
- Year 4:
[tex]\[ \text{Interest}_4 = 9447.84 \times 0.08 = 755.8272 \][/tex]
[tex]\[ \text{Balance}_4 = 9447.84 + 755.8272 = 10203.6672 \][/tex]
- Year 5:
[tex]\[ \text{Interest}_5 = 10203.6672 \times 0.08 = 816.293376 \][/tex]
[tex]\[ \text{Balance}_5 = 10203.6672 + 816.293376 = 11019.960576 \][/tex]
Here's the completed table:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Year} & \begin{array}{c} \text{Suzanne's} \\ \text{Annual} \\ \text{Interest} \end{array} & \begin{array}{c} \text{Suzanne's} \\ \text{Balance} \end{array} & \begin{array}{c} \text{Derek's} \\ \text{Annual} \\ \text{Interest} \end{array} & \begin{array}{c} \text{Derek's} \\ \text{Balance} \end{array} \\ \hline 1 & 600.0 & 8100.0 & 600.0 & 8100.0 \\ 2 & 600.0 & 8700.0 & 648.0 & 8748.0 \\ 3 & 600.0 & 9300.0 & 699.84 & 9447.84 \\ 4 & 600.0 & 9900.0 & 755.8272 & 10203.6672 \\ 5 & 600.0 & 10500.0 & 816.293376 & 11019.960576 \\ \hline \end{array} \][/tex]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
