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Part 1
Julie borrowed ​$1 comma 900 for 8 months from a bank. The bank discounted the loan at 3.5 %.
a. How much interest did Julie pay the bank for the use of its​ money?
b. How much did she receive from the​ bank?
c. What was the actual rate of interest she​ paid?


We are given that Julie borrowed $1,900 for 8 months, and the bank discounted the loan at 3.5%. We need to calculate the interest Julie paid, the amount she received, and the actual rate of interest she paid.

### Part (a): Interest Paid by Julie
To calculate the interest, we will use the formula for a discount loan:

\[
\text{Interest} = \text{Principal} \times \text{Discount Rate} \times \text{Time}
\]

Here:
- Principal = $1,900
- Discount Rate = 3.5% = 0.035
- Time = 8 months = $ \frac{8}{12} $ years

\[
\text{Interest} = 1900 \times 0.035 \times \frac{8}{12}
\]

Let me calculate that for you.The interest Julie paid to the bank is approximately **$44.33**.

### Part (b): Amount Julie Received from the Bank
The amount Julie received is the principal amount minus the interest that was deducted upfront by the bank:

\[
\text{Amount received} = \text{Principal} - \text{Interest}
\]

Let me calculate that for you.Julie received approximately **$1,855.67** from the bank after the interest was deducted.

### Part (c): Actual Rate of Interest
The actual rate of interest is the effective interest rate, which is calculated based on the amount Julie received rather than the principal. The formula for the actual interest rate is:

\[
\text{Actual Interest Rate} = \frac{\text{Interest Paid}}{\text{Amount Received}} \times \frac{12}{\text{Months}}
\]

Substituting the values:

\[
\text{Actual Interest Rate} = \frac{44.33}{1855.67} \times \frac{12}{8}
\]

Let me calculate that.The actual rate of interest Julie paid is approximately **3.58%**.

### Summary:
- **(a)** Julie paid **$44.33** in interest to the bank.
- **(b)** She received **$1,855.67** after the discount.
- **(c)** The actual rate of interest Julie paid is approximately **3.58%**.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the interest change if the loan duration was extended to 12 months?
2. What happens if the discount rate increases to 5%?
3. How does a discount loan differ from a regular interest loan?
4. If Julie borrowed $3,000 under the same conditions, what would her interest be?
5. What is the total amount paid by Julie at the end of the loan period?

**Tip**: For discount loans, the bank deducts interest upfront, reducing the amount you receive initially but not the total amount you owe.

Julie borrowed $1,900 for 8 months from a bank. The bank discounted the loan at 3.5%. a. How much interest did Julie pay the bank for the use of its money? b. How much did she receive from the bank? c. What was the actual rate of interest she paid?

Explore how Julie calculates interest, the amount received, and the actual interest rate for a loan of $1,900 discounted at 3.5%. This problem covers key financial math concepts, including simple interest, percentage calculation, and discount loans. Ideal for students in Grades 9-12.

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