You have an investment of $5,000 at a quarterly simple interest rate of 2%. How much will the investment be worth after 1 year?

To calculate the future value of an investment under simple interest, we use the formula:

\[
A = P(1 + rt)
\]

Where:
- $A$ is the amount (future value) after interest,
- $P$ is the principal (initial investment),
- $r$ is the interest rate per period,
- $t$ is the time (in periods).

In this case:
- $P = 5000$,
- The quarterly interest rate is 2% (or $r = 0.02$),
- 1 year equals 4 quarters, so $t = 4$.

Now, applying the formula:

\[
A = 5000 \times (1 + 0.02 \times 4)
\]
\[
A = 5000 \times (1 + 0.08)
\]
\[
A = 5000 \times 1.08 = 5400
\]

So, after 1 year, the investment will be worth **$5,400**.

Would you like more details or have any other questions?

Here are 5 related questions:
1. What would the investment be worth after 2 years?
2. How would the result change if the interest were compounded quarterly instead?
3. What is the total interest earned after 1 year?
4. How does the investment compare with a different rate, say 3% per quarter?
5. How does simple interest differ from compound interest?

**Tip:** In simple interest, the interest is always calculated on the original principal, while compound interest grows by adding interest to the principal over time.

Learn how to calculate the future value of a $5,000 investment at a quarterly simple interest rate of 2% over 1 year. This problem uses the simple interest formula A = P(1 + rt), demonstrating key algebraic principles for students in Grades 9-10.

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