Answer :
- Calculate the time in years: $t = \frac{193}{365}$.
- Calculate the simple interest: $I = Prt = 5700 \times 0.12 \times \frac{193}{365} = 361.68$.
- Calculate the total amount owed: $A = P + I = 5700 + 361.68 = 6061.68$.
- The interest owed is $\boxed{361.68}$ and the total amount owed is $\boxed{6061.68}$.
### Explanation
1. Understanding the Problem
We are given that the print shop borrows $\$5700$ from a credit union for 193 days. The credit union charges simple interest at an annual rate of $12\%$ for this loan. We need to find the interest owed after 193 days and the total amount owed after 193 days.
2. Calculating Time in Years
First, we need to calculate the time in years. Since each day is $\frac{1}{365}$ of a year, the time in years is $\frac{193}{365}$.
3. Calculating the Interest
Next, we calculate the interest owed using the simple interest formula: $I = Prt$, where $P = 5700$, $r = 0.12$, and $t = \frac{193}{365}$. So, $I = 5700 \times 0.12 \times \frac{193}{365}$.
4. Finding the Interest Owed
Calculating the value of I, we get $I = 5700 \times 0.12 \times \frac{193}{365} = 361.67671232876717$. Rounding to the nearest cent, the interest owed is $\$361.68$.
5. Calculating the Total Amount Owed
Now, we calculate the total amount owed after 193 days. The total amount owed is the principal plus the interest: $A = P + I$, where $P = 5700$ and $I = 361.68$. So, $A = 5700 + 361.68$.
6. Finding the Total Amount Owed
Calculating the value of A, we get $A = 5700 + 361.68 = 6061.676712328767$. Rounding to the nearest cent, the total amount owed is $\$6061.68$.
7. Final Answer
Therefore, the interest owed after 193 days is $\$361.68$, and the total amount owed after 193 days is $\$6061.68$.
### Examples
Understanding simple interest is crucial in many real-life financial situations. For instance, when you take out a loan for a car or a house, the lender will charge interest on the principal amount. Knowing how to calculate simple interest helps you determine the total cost of borrowing and allows you to compare different loan options. It's also applicable in savings accounts where you earn interest on your deposits, helping you understand how your savings grow over time.
- Calculate the simple interest: $I = Prt = 5700 \times 0.12 \times \frac{193}{365} = 361.68$.
- Calculate the total amount owed: $A = P + I = 5700 + 361.68 = 6061.68$.
- The interest owed is $\boxed{361.68}$ and the total amount owed is $\boxed{6061.68}$.
### Explanation
1. Understanding the Problem
We are given that the print shop borrows $\$5700$ from a credit union for 193 days. The credit union charges simple interest at an annual rate of $12\%$ for this loan. We need to find the interest owed after 193 days and the total amount owed after 193 days.
2. Calculating Time in Years
First, we need to calculate the time in years. Since each day is $\frac{1}{365}$ of a year, the time in years is $\frac{193}{365}$.
3. Calculating the Interest
Next, we calculate the interest owed using the simple interest formula: $I = Prt$, where $P = 5700$, $r = 0.12$, and $t = \frac{193}{365}$. So, $I = 5700 \times 0.12 \times \frac{193}{365}$.
4. Finding the Interest Owed
Calculating the value of I, we get $I = 5700 \times 0.12 \times \frac{193}{365} = 361.67671232876717$. Rounding to the nearest cent, the interest owed is $\$361.68$.
5. Calculating the Total Amount Owed
Now, we calculate the total amount owed after 193 days. The total amount owed is the principal plus the interest: $A = P + I$, where $P = 5700$ and $I = 361.68$. So, $A = 5700 + 361.68$.
6. Finding the Total Amount Owed
Calculating the value of A, we get $A = 5700 + 361.68 = 6061.676712328767$. Rounding to the nearest cent, the total amount owed is $\$6061.68$.
7. Final Answer
Therefore, the interest owed after 193 days is $\$361.68$, and the total amount owed after 193 days is $\$6061.68$.
### Examples
Understanding simple interest is crucial in many real-life financial situations. For instance, when you take out a loan for a car or a house, the lender will charge interest on the principal amount. Knowing how to calculate simple interest helps you determine the total cost of borrowing and allows you to compare different loan options. It's also applicable in savings accounts where you earn interest on your deposits, helping you understand how your savings grow over time.
