Suppose that a loan of $3000 is given at an interest rate of 18% compounded each year. Assume that no payments are made on the loan. Follow the instructions below. Do not do any rounding. (a) Find the amount owed at the end of 1 year. (b) Find the amount owed at the end of 2 years.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Linear Equations: Introduction to Compound Interest
#### Scenario
Suppose that a loan of $3000 is given at an interest rate of 18% compounded each year. Assume that no payments are made on the loan.
#### Instructions
Follow the instructions below. Do not do any rounding.
#### Questions
1. **Find the amount owed at the end of 1 year.**
- Amount: $ ___________
2. **Find the amount owed at the end of 2 years.**
- Amount: $ ___________
### Explanation
To calculate the amount owed with compounded interest, use the formula:
\[ A = P(1 + \frac{r}{n})^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial sum of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested or borrowed for, in years.
For this scenario:
- \( P = 3000 \) (initial loan)
- \( r = 0.18 \) (18% interest rate)
- \( n = 1 \) (compounded annually)
- \( t = 1 \) for part (a) and \( t = 2 \) for part (b)
Insert these values into the formula to find the amounts owed for parts (a) and (b).
#### Note
Interactivity involves filling in the computed amounts in the text boxes provided. Use the 'Check' button to verify your answers after calculation, and utilize other functions like 'Explanation' for detailed problem-solving steps if needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5c408b24-72ca-4f3d-857b-96deb6fc7977%2Ff865ed3e-7cb0-474d-8783-a17ebf88d245%2Fp2wds8w_processed.jpeg&w=3840&q=75)
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