Two years ago, you invested $3,150. Today, it is worth $3,900. What rate of interest did you earn?

Multiple Choice

11.27%

5.20%

.94%

5.64%

4.20%

To find the rate of interest earned, we can use the formula for compound interest, assuming the investment was compounded annually:

\[
A = P(1 + r)^t
\]

Where:
- $ A $ is the final amount ($3,900),
- $ P $ is the initial principal ($3,150),
- $ r $ is the annual interest rate (expressed as a decimal),
- $ t $ is the time in years (2 years).

We need to solve for $ r $. First, rearrange the formula to isolate $ r $:

\[
\frac{A}{P} = (1 + r)^t
\]

\[
\frac{3,900}{3,150} = (1 + r)^2
\]

\[
1.2381 = (1 + r)^2
\]

Now, take the square root of both sides:

\[
\sqrt{1.2381} = 1 + r
\]

\[
1.1127 = 1 + r
\]

Now, subtract 1 from both sides:

\[
r = 0.1127
\]

Convert $ r $ to a percentage:

\[
r = 11.27\%
\]

Thus, the interest rate is **11.27%**.

Would you like further details or have any questions?

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Here are 5 related questions:
1. How would the formula change for monthly compounding?
2. How would the interest rate change if the investment period was longer?
3. What is the formula for continuously compounded interest?
4. How does compound interest differ from simple interest?
5. Can interest rates vary within a fixed investment period?

**Tip:** Always ensure the time period $ t $ aligns with how the interest is compounded (annually, monthly, etc.).

Two years ago, you invested $3,150. Today, it is worth $3,900. What rate of interest did you earn?

Learn how to calculate the compound interest rate when an investment grows from $3,150 to $3,900 over 2 years. This detailed solution uses the compound interest formula and algebraic manipulation to find that the interest rate is 11.27%. Suitable for students in Grades 9-12.

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