Discover a wealth of knowledge at Westonci.ca, where experts provide answers to your most pressing questions. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
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 visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
