A radio commercial for a loan company​ states: "You only pay 32 cents a day for each​ $500 borrowed." If you borrow $ 2,302 for 168 ​days, what amount will you​ repay, and what annual interest rate is the company actually​ charging? (Assume a​ 360-day year.) Round the final answer to two decimal points.



Let's break down this problem step by step:

### Step 1: Calculate the total daily cost
According to the commercial, you pay **32 cents a day for each $500 borrowed**. First, let's calculate the cost per day for the borrowed amount.

You borrowed $2,302. To find how many units of $500 are in $2,302:

\[
\frac{2,302}{500} = 4.604
\]

So, you're paying for approximately 4.604 units of $500 each day.

### Step 2: Calculate the total cost per day
Since the cost is 32 cents per $500 per day, multiply the number of units (4.604) by the cost per unit (32 cents or $0.32):

\[
4.604 \times 0.32 = 1.47328 \text{ dollars per day}
\]

### Step 3: Calculate the total repayment amount
You are borrowing the money for 168 days. To find the total amount you will pay for these 168 days, multiply the daily cost by the number of days:

\[
1.47328 \times 168 = 247.51776
\]

This is the total amount in interest that you will pay over 168 days. Adding this to the original amount borrowed ($2,302):

\[
2,302 + 247.51776 = 2,549.52
\]

So, the total repayment amount is **$2,549.52**.

### Step 4: Calculate the annual interest rate
Now, let's calculate the annual interest rate based on this repayment. The interest paid is $247.52 over 168 days. To annualize this interest rate, we need to convert it to a 360-day year.

First, calculate the interest rate for the 168-day period:

\[
\frac{247.52}{2,302} \times 100 = 10.75\% \text{ (for 168 days)}
\]

Now, to find the annual interest rate, scale this up to a full 360-day year:

\[
\frac{360}{168} \times 10.75 = 23.04\%
\]

### Final Answer:
- The total amount you will repay is **$2,549.52**.
- The annual interest rate is **23.04%**.

Would you like more details or clarifications on any part of this?

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**Related questions:**
1. How would the total repayment change if the loan period was 200 days?
2. What would be the repayment amount if only $1,000 was borrowed for the same period?
3. How does the interest rate change if the daily cost per $500 borrowed is 40 cents?
4. What is the formula to calculate the annual interest rate for any borrowed amount and daily cost?
5. How would the annual interest rate change if the loan was repaid in 120 days instead of 168?

**Tip:** Always break down problems into smaller steps to simplify calculations and ensure accuracy.

A radio commercial for a loan company​ states: 'You only pay 32 cents a day for each​ $500 borrowed.' If you borrow $2,302 for 168 ​days, what amount will you​ repay, and what annual interest rate is the company actually​ charging? (Assume a​ 360-day year.) Round the final answer to two decimal points.

Learn how to calculate the total repayment amount and the annual interest rate for a loan of $2,302 borrowed over 168 days at a daily cost of 32 cents per $500. This problem covers key concepts in interest calculation, suitable for students in Grades 9-12.

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