double the rate and use your classmate’s principle and time to find the new account value.Hello everyone,

For this week I have Choose your principal and time and solve for the rate:

So say I have the amount of $5000 at the time of 3 years with $789 earned in interest. I want to know the rate of my interest?

my formula would be (principal) x (rate) x (time) /100

1) plug in your information into the formula  5000 x r x 3 /100

2) multiply 5000 x 3=15,000

3) 15,000/100=150

789=150 x r

4) you now have interest earned equals 150 x r. Now you must divide each side by 150

789/150=150 x r/150

r=5.26%

It looks like you're calculating the interest rate based on a given principal, time, and interest earned using the **simple interest formula**:

\[
\text{Simple Interest} = \frac{P \times r \times t}{100}
\]

Where:
- $ P $ is the principal (initial amount),
- $ r $ is the rate of interest (as a percentage),
- $ t $ is the time (in years),
- Simple Interest is the interest earned.

Given:
- Principal ($ P $) = $5000,
- Time ($ t $) = 3 years,
- Interest earned = $789.

### Step-by-Step Calculation:

1. The formula is $ \frac{5000 \times r \times 3}{100} = 789 $.
2. Simplifying $ 5000 \times 3 = 15000 $, so:
   \[
   \frac{15000 \times r}{100} = 789
   \]
3. Dividing both sides by 150:
   \[
   r = \frac{789}{150} = 5.26\%
   \]

So, the interest rate is **5.26%**.

### Now, to double the rate:

1. Doubling the rate means the new rate would be $ 2 \times 5.26\% = 10.52\% $.
2. We use the same principal ($5000) and time (3 years) to find the new account value with the doubled rate.
   - New interest = $ \frac{5000 \times 10.52 \times 3}{100} $.
   - Simplifying: $ 5000 \times 10.52 \times 3 = 157800 $, then divide by 100: 
     \[
     \text{New Interest} = \frac{157800}{100} = 1578
     \]

Thus, with the new interest rate, the interest earned will be **$1578**.

### New Account Value:
\[
\text{New Account Value} = 5000 + 1578 = 6578
\]

The new account value would be **$6578** after 3 years with the doubled interest rate.

---

Do you need further details or have any questions? Here are 5 questions to deepen understanding:

1. How does simple interest differ from compound interest?
2. What happens to the account value if the interest rate is halved instead of doubled?
3. Can you solve the formula using different values for time, like 5 or 10 years?
4. How would compound interest affect the total amount in this case?
5. What are some factors that influence interest rates in real-life financial markets?

**Tip:** When interest rates increase, so does the total interest earned, but be aware of how long you're leaving the money in the account, as time plays a big role too!

For this week I have Choose your principal and time and solve for the rate: So say I have the amount of $5000 at the time of 3 years with $789 earned in interest. I want to know the rate of my interest? My formula would be (principal) x (rate) x (time) /100.

Learn how to calculate the simple interest rate when $5000 is invested over 3 years with $789 earned in interest. This detailed guide breaks down the simple interest formula and shows a step-by-step solution to find the interest rate, suitable for high school students in Grades 9-12.

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