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Let's go over each question on this worksheet to verify and explain the calculations for simple interest.

### Given Information:
The simple interest formula is:
\[
I = P \times r \times t
\]
where:
- $ P $ is the principal (initial amount of money invested),
- $ r $ is the interest rate (as a decimal),
- $ t $ is the time (in years).

If asked to find the amount of the investment after interest, we use:
\[
A = P + I
\]

---

### Problem Breakdown:

#### 1. How much is earned if $6500 is invested at 8.5% simple interest for 6 months?
   - **Given:**
     - $ P = 6500 $
     - $ r = 8.5\% = \frac{8.5}{100} = 0.085 $
     - $ t = 6 \text{ months} = 0.5 \text{ years} $

   - **Solution:**
     - Calculate $ I $ using $ I = P \times r \times t $:
       \[
       I = 6500 \times 0.085 \times 0.5 = 276.25
       \]
     - **Answer:** The interest earned is **$276.25**.

#### 2. How much is the investment now worth?
   - To find the total amount $ A $, use $ A = P + I $:
     \[
     A = 6500 + 276.25 = 6776.25
     \]
   - **Answer:** The investment is now worth **$6776.25**.

#### 3. How long should $3500 be invested for in a 7% simple interest account to earn $1000 in interest?
   - **Given:**
     - $ P = 3500 $
     - $ r = 7\% = 0.07 $
     - $ I = 1000 $

   - **Solution:**
     - Rearrange the formula $ I = P \times r \times t $ to solve for $ t $:
       \[
       t = \frac{I}{P \times r} = \frac{1000}{3500 \times 0.07}
       \]
       \[
       t = \frac{1000}{245} \approx 4.08 \text{ years}
       \]
     - **Answer:** The investment should be made for **4.08 years** to earn $1000 in interest.

#### 4. What simple interest rate is needed to make $6000 grow to $10000 over the course of 10 years?
   - **Given:**
     - $ P = 6000 $
     - $ A = 10000 $ (so $ I = 10000 - 6000 = 4000 $)
     - $ t = 10 $ years

   - **Solution:**
     - Rearrange the formula $ I = P \times r \times t $ to solve for $ r $:
       \[
       r = \frac{I}{P \times t} = \frac{4000}{6000 \times 10}
       \]
       \[
       r = \frac{4000}{60000} = 0.0667
       \]
       \[
       r = 0.0667 \times 100 = 6.67\%
       \]
     - **Answer:** A simple interest rate of **6.67%** per year is required.

---

Would you like further details on any specific question, or have any additional questions?

### Follow-up Questions:
1. How would the calculations change if interest were compounded instead of simple?
2. What is the impact of a higher interest rate on the time needed to reach a specific interest amount?
3. How can you verify the interest rate calculated in question 4?
4. What formula adjustment is needed if the interest is calculated monthly instead of annually?
5. Can the simple interest formula be applied if the interest rate changes over time?

### Tip:
Always convert the rate to a decimal (by dividing by 100) and time to years for accuracy in simple interest problems.

Personal Finance Review worksheet involving simple interest problems including calculating interest earned, total investment value, required investment time, and interest rate.

This worksheet provides a personal finance review with simple interest calculations. Learn how to calculate interest earned, determine total investment value, and find required time or interest rate for a target amount. Suitable for high school students in Grades 9-12.

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