You invested $18,000 in an account paying 3.5% annual interest. Find the total value after 3 years when the interest is compounded quarterly. (Round to two decimal places)


To find the total value of the investment after 3 years with interest compounded quarterly, we use the compound interest formula:

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

Where:
- $A$ is the amount of money accumulated after $t$ years, including interest.
- $P$ is the principal amount (initial investment) = $18,000.
- $r$ is the annual interest rate (decimal) = 3.5% = 0.035.
- $n$ is the number of times the interest is compounded per year = 4 (since it is compounded quarterly).
- $t$ is the time the money is invested for, in years = 3 years.

Now, let's plug in the values:

\[
A = 18000 \left(1 + \frac{0.035}{4}\right)^{4 \times 3}
\]

\[
A = 18000 \left(1 + 0.00875\right)^{12}
\]

\[
A = 18000 \left(1.00875\right)^{12}
\]

Now calculate $ (1.00875)^{12} $:

\[
1.00875^{12} \approx 1.10944
\]

Then multiply by the principal:

\[
A = 18000 \times 1.10944 = 19969.92
\]

So, the total value of the investment after 3 years is approximately **$19,969.92**.

Would you like more details or have any questions?

Here are 5 related questions to explore further:
1. What is the formula for simple interest, and how does it differ from compound interest?
2. How would the total amount change if the interest were compounded monthly instead of quarterly?
3. What would the value be if the investment was for 5 years instead of 3 years?
4. How can we calculate the interest earned only, separate from the total investment?
5. How would changing the interest rate to 5% affect the final amount?

**Tip:** The more frequently the interest is compounded, the more interest is accumulated over time.

You invested $18,000 in an account paying 3.5% annual interest. Find the total value after 3 years when the interest is compounded quarterly. (Round to two decimal places)

Find out how to calculate the total value of an $18,000 investment with a 3.5% annual interest rate compounded quarterly over 3 years. Learn to apply the compound interest formula for accurate financial planning. Suitable for students in Grades 9-12.

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