Suppose that you invest $112,300 today. How much will this amount be worth in seven 
years if the interest rate is 7%? How would your answer change if the interest rate is 9%?

We can solve this problem using the formula for compound interest:

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

Where:
- $A$ is the amount of money after interest.
- $P$ is the principal or initial investment (in this case, $112,300).
- $r$ is the annual interest rate (expressed as a decimal).
- $n$ is the number of times interest is compounded per year (assuming it's compounded annually, so $n = 1$).
- $t$ is the time in years.

### Case 1: Interest Rate = 7%

Using $r = 0.07$, $t = 7$, and $n = 1$:

\[
A = 112,300 \times \left(1 + \frac{0.07}{1}\right)^{1 \times 7}
\]

\[
A = 112,300 \times (1.07)^7
\]

Let's calculate that:

\[
A \approx 112,300 \times 1.60578 \approx 180,379.21
\]

So, after 7 years at an interest rate of 7%, the investment will be worth approximately **$180,379.21**.

### Case 2: Interest Rate = 9%

Using $r = 0.09$, $t = 7$, and $n = 1$:

\[
A = 112,300 \times \left(1 + \frac{0.09}{1}\right)^{1 \times 7}
\]

\[
A = 112,300 \times (1.09)^7
\]

Let's calculate that:

\[
A \approx 112,300 \times 1.82804 \approx 205,264.08
\]

So, after 7 years at an interest rate of 9%, the investment will be worth approximately **$205,264.08**.

### Summary:
- At 7% interest, the investment grows to **$180,379.21**.
- At 9% interest, the investment grows to **$205,264.08**.

Would you like more details on any part of this calculation?

Here are 5 related questions you might find helpful:
1. How does compounding frequency affect the final amount?
2. What would happen if the investment period was longer than 7 years?
3. What is the formula for continuous compounding, and how would it apply here?
4. How can I compare investments with different interest rates?
5. How does inflation impact the real value of the future investment?

**Tip**: The earlier you invest, the more you benefit from the power of compounding! Start early to maximize returns.

Suppose that you invest $112,300 today. How much will this amount be worth in seven years if the interest rate is 7%? How would your answer change if the interest rate is 9%?

Discover how an investment of $112,300 grows over 7 years with 7% and 9% interest rates. Learn the compound interest formula and how to apply it to calculate the future value of investments. This detailed solution is perfect for high school students studying exponential growth and finance.

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