For her 1st birthday Jamie's parents invested $7,000.00 in an 15-year certificate for her that pays 5% compounded every 4 months. How much is the certificate worth on Jamie's 16 birthday?

To calculate the future value of Jamie's certificate, we can use the formula for compound interest:

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

Where:
- $ A $ is the future value of the investment (what we're solving for),
- $ P $ is the principal (initial amount invested), which is \$7,000,
- $ r $ is the annual interest rate (5% or 0.05),
- $ n $ is the number of times the interest is compounded per year (since it's compounded every 4 months, there are 3 periods per year),
- $ t $ is the number of years the money is invested (15 years).

### Step-by-Step Calculation

1. **Principal**: $ P = 7,000 $
2. **Annual interest rate**: $ r = 0.05 $
3. **Compounding periods per year**: $ n = 3 $ (since the interest is compounded every 4 months)
4. **Time in years**: $ t = 15 $

Now, substituting these values into the formula:

\[
A = 7,000 \left( 1 + \frac{0.05}{3} \right)^{3 \times 15}
\]

Let's compute the value.The certificate will be worth approximately \$14,727.68 on Jamie's 16th birthday.

Would you like any further details or have any questions?

Here are five related questions to deepen your understanding:

1. How would the future value change if the interest were compounded monthly instead of every 4 months?
2. What would happen to the future value if the interest rate increased to 6%?
3. How much interest did Jamie's certificate earn over the 15 years?
4. What is the formula for continuous compounding, and how would it affect the outcome?
5. How would the future value change if the investment period were 20 years instead of 15?

**Tip:** The more frequently interest is compounded, the higher the final amount will be due to compounding effects.

For her 1st birthday Jamie's parents invested $7,000.00 in a 15-year certificate for her that pays 5% compounded every 4 months. How much is the certificate worth on Jamie's 16th birthday?

Learn how to calculate the future value of a $7,000 investment over 15 years at a 5% interest rate, compounded every 4 months. This compound interest problem uses key financial formulas and is suitable for students in Grades 10-12.

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