Terry deposited $8500 in a CD paying 8% interest compounded quarterly. Find the value of the account after 7 ½ years. Show the formula with correct numbers for the variables.

To find the value of the account after 7 ½ years with interest compounded quarterly, we use the formula for compound interest:

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

where:
- $ A $ is the amount of money accumulated after $ t $ years, 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:
- $ P = 8500 $ (the initial deposit)
- $ r = 0.08 $ (the annual interest rate, 8%)
- $ n = 4 $ (interest is compounded quarterly)
- $ t = 7.5 $ (the time period is 7 ½ years)

Substitute these values into the formula:

\[ A = 8500 \left(1 + \frac{0.08}{4}\right)^{4 \times 7.5} \]

Calculate the values inside the parentheses first:

\[ \frac{0.08}{4} = 0.02 \]

\[ A = 8500 \left(1 + 0.02\right)^{30} \]

\[ A = 8500 \left(1.02\right)^{30} \]

Next, calculate $ (1.02)^{30} $:

\[ (1.02)^{30} \approx 1.81136 \]

Now, multiply by the principal amount:

\[ A = 8500 \times 1.81136 \]

\[ A \approx 15396.56 \]

Therefore, the value of the account after 7 ½ years is approximately $15,396.56.

Would you like more details or have any questions?

Here are 5 more questions you can ask:
1. How is continuous compounding different from quarterly compounding?
2. Can you explain the derivation of the compound interest formula?
3. How do you calculate the effective annual rate (EAR) from a nominal rate?
4. What happens to the future value if the compounding frequency increases?
5. How does the principal amount affect the future value in compound interest?

**Tip:** When dealing with compound interest, always check the compounding frequency as it significantly affects the final amount.

Learn how to calculate the value of an investment after 7 ½ years with an initial deposit of $8500, earning 8% interest compounded quarterly. This problem uses the compound interest formula and covers concepts of interest compounding and exponential growth. Suitable for high school students.

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