Lynne needs to borrow $5000 for cosmetic surgery. She obtains a loan from her grandmother for 39 months at a simple annual interest rate of 7.7%.
How much will Lynne pay back her grandmother?

$ Round to the nearest cent

To calculate the total amount Lynne will pay back her grandmother, we can use the formula for simple interest:

\[
I = P \times r \times t
\]

Where:
- $I$ is the interest,
- $P$ is the principal amount ($5000),
- $r$ is the annual interest rate (7.7% or 0.077 as a decimal),
- $t$ is the time in years (39 months = $ \frac{39}{12} $ years).

First, let's calculate the interest:

\[
t = \frac{39}{12} = 3.25 \text{ years}
\]

Now, substitute the values into the simple interest formula:

\[
I = 5000 \times 0.077 \times 3.25
\]

Now let's calculate that amount.The interest Lynne will pay on the loan is $1,251.25.

Now, to find the total amount Lynne will pay back her grandmother, we add the interest to the principal:

\[
\text{Total amount} = P + I = 5000 + 1251.25 = 6251.25
\]

So, Lynne will pay back **$6,251.25**.

Would you like further details or have any questions?

Here are 5 related questions to think about:
1. What would happen if the interest rate was compounded instead of simple interest?
2. How much would the interest be if the loan was paid back in 2 years instead of 39 months?
3. How does the interest rate affect the total amount paid over different time periods?
4. What happens to the interest if the loan amount is increased to $10,000?
5. How can Lynne reduce the amount she pays in interest?

**Tip:** Simple interest is calculated only on the principal amount, while compound interest calculates interest on both the principal and any accumulated interest.

Lynne needs to borrow $5000 for cosmetic surgery. She obtains a loan from her grandmother for 39 months at a simple annual interest rate of 7.7%. How much will Lynne pay back her grandmother?

Learn how to calculate the total amount Lynne will pay back on a $5000 loan over 39 months at a 7.7% annual simple interest rate. This example covers simple interest calculation, time conversion, and key algebraic concepts. Suitable for Grades 9-10.

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