https://file.aiquickdraw.com/mathbot/file/1728938653756ybp52tnh.jpg

The problem asks about the amount of money you will receive upfront for a discount loan with simple interest. The loan details are:

- Loan amount: $3,900.00
- Annual simple interest rate: 7%
- Time period: 11 months

This is a **discount loan**, meaning the interest is subtracted from the principal at the beginning. To calculate how much you will receive at the start, follow these steps:

### Step 1: Calculate the interest
The formula for simple interest is:
\[
I = P \times r \times t
\]
Where:
- $ P $ is the principal amount ($3,900),
- $ r $ is the annual interest rate (7% or 0.07),
- $ t $ is the time in years. Since the time given is 11 months, convert that to years: $ t = \frac{11}{12} $.

Now calculate the interest:
\[
I = 3900 \times 0.07 \times \frac{11}{12}
\]
\[
I = 3900 \times 0.07 \times 0.9167 \approx 250.25
\]
The interest is approximately **$250.25**.

### Step 2: Subtract the interest from the loan amount
Since this is a discount loan, the interest is deducted upfront:
\[
\text{Amount received} = 3900 - 250.25 = 3649.75
\]

So, you will receive approximately **$3,649.75** at the start of the loan.

Would you like further details or clarification?

---

Here are 5 related questions you can explore:
1. How does the formula for simple interest change for different compounding periods?
2. What would happen to the amount received if the loan term were longer or shorter?
3. How does a discount loan compare to a regular loan in terms of total interest paid?
4. What if the interest rate were 10% instead of 7%—how much would be received?
5. How would the result change if the loan term were calculated in days instead of months?

**Tip**: Always make sure to convert the time period to years when calculating interest for loans or investments.

If you are charged 7% (annual rate) simple interest on a discount loan for $3,900.00, paying it back in 11 months, how much money will you actually receive at the start of the loan?

This problem demonstrates how to calculate the amount received at the start of a $3,900 discount loan with a 7% annual simple interest rate over 11 months. Includes step-by-step calculation of interest and final amount received.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation