Question 6 options:
Do NOT type the $ sign in your answers. Make sure you round correctly, to the nearest DOLLAR, or the quiz will not recognize your answer as correct.

An account pays 3.64% interest, compounded bi-weekly. Tyler invests money into this account and after 3 years, the value has grown to $4225.

a) How much did he invest?

b) How much interest was earned?

To solve this problem, we need to use the formula for compound interest:

\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]

where:
- $ A $ is the amount of money accumulated after n periods, including interest.
- $ P $ is the principal amount (the initial amount of money).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times that interest is compounded per year.
- $ t $ is the time the money is invested for, in years.

Given:
- $ A = 4225 $
- $ r = 3.64\% = 0.0364 $
- $ n = 26 $ (since interest is compounded bi-weekly, and there are 52 weeks in a year)
- $ t = 3 $

First, we solve for $ P $:

\[ 4225 = P \left(1 + \frac{0.0364}{26}\right)^{26 \times 3} \]

Simplify the equation step-by-step to isolate $ P $:

1. Calculate the bi-weekly interest rate:
\[ 1 + \frac{0.0364}{26} \approx 1 + 0.0014 = 1.0014 \]

2. Calculate the exponent:
\[ 26 \times 3 = 78 \]

3. Raise the interest rate to the power of the number of compounding periods:
\[ (1.0014)^{78} \approx 1.114 \]

4. Rearrange to solve for $ P $:
\[ P = \frac{4225}{1.114} \approx 3792 \]

Round $ P $ to the nearest dollar:
\[ P \approx 3792 \]

So, Tyler invested approximately $ 3792 $ dollars.

Next, to find the interest earned:

b) Calculate the interest earned by subtracting the principal from the amount accumulated:
\[ \text{Interest Earned} = A - P = 4225 - 3792 = 433 \]

Thus, the interest earned is approximately $ 433 $ dollars.

**Summary:**
a) The amount Tyler invested is approximately 3792 dollars.
b) The interest earned is approximately 433 dollars.

Do you want more details or have any questions?

Here are 5 numbered questions you can ask:
1. How do you calculate the compound interest for different compounding periods?
2. What is the difference between simple interest and compound interest?
3. How can we adjust the formula for different compounding intervals like monthly or quarterly?
4. Can you show the step-by-step process for another example of compound interest calculation?
5. What are some common mistakes to avoid when calculating compound interest?

**Tip:** Always make sure to convert the percentage interest rate to a decimal form by dividing by 100 before using it in calculations.

Learn how to calculate compound interest with bi-weekly compounding using the formula. Solve for the principal amount and interest earned over a specified time period. Suitable for high school students and anyone interested in financial mathematics.

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