**Mrs. Tracy took a loan of $2500 from a bank** 


**with simple interest. After 4 years, she has to pay back $3000.** 


**The rate of her loan?**

We can solve this problem using the simple interest formula:

\[
A = P(1 + rt)
\]

Where:
- $ A $ is the total amount to be paid back (including interest),
- $ P $ is the principal amount (the loan amount),
- $ r $ is the rate of interest per year (as a decimal),
- $ t $ is the time in years.

In this case:
- $ A = 3000 $ (amount to be paid back),
- $ P = 2500 $ (initial loan amount),
- $ t = 4 $ years.

### Step 1: Plug in the values
\[
3000 = 2500(1 + r \cdot 4)
\]

### Step 2: Simplify the equation
\[
3000 = 2500(1 + 4r)
\]

### Step 3: Divide both sides by 2500
\[
1.2 = 1 + 4r
\]

### Step 4: Subtract 1 from both sides
\[
0.2 = 4r
\]

### Step 5: Solve for $ r $
\[
r = \frac{0.2}{4} = 0.05
\]

Thus, the rate of interest is **5% per year**.

Would you like further details or clarifications?

---

Here are 5 related questions for deeper understanding:
1. What is the formula for calculating compound interest?
2. How does simple interest differ from compound interest?
3. What would the total amount be if the interest rate were 6% instead of 5%?
4. How long would it take to repay $3000 at the same rate if Mrs. Tracy borrowed $2000 instead?
5. What happens to the interest if the time is doubled but the rate stays the same?

**Tip:** Always ensure you convert the interest rate to a decimal before applying it in formulas (e.g., 5% = 0.05).

Mrs. Tracy took a loan of $2500 from a bank with simple interest. After 4 years, she has to pay back $3000. What is the rate of her loan?

Learn how to calculate the interest rate for a $2500 loan with simple interest over 4 years, where the total repayment amount is $3000. This problem involves algebraic concepts and the simple interest formula. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation