If an investment grew to $15,500 in 2 years and the interest amount earned was $950, calculate the nominal interest rate compounded monthly.
%
Round to two decimal places

To find the nominal interest rate compounded monthly, we can use the compound interest formula:

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

Where:
- $A$ is the final amount (\$15,500).
- $P$ is the principal amount (this will be $A - \text{Interest}$).
- $r$ is the nominal interest rate (what we're solving for).
- $n$ is the number of compounding periods per year (monthly, so $n = 12$).
- $t$ is the time in years (2 years).

### Step 1: Find the principal amount ($P$)
The interest earned was \$950, so the principal is:

\[
P = A - \text{Interest} = 15,500 - 950 = 14,550
\]

### Step 2: Plug in the values into the compound interest formula

We have:
\[
A = 15,500, \quad P = 14,550, \quad t = 2, \quad n = 12
\]

Substitute into the formula:

\[
15,500 = 14,550 \left(1 + \frac{r}{12}\right)^{12 \times 2}
\]

Simplifying:

\[
15,500 = 14,550 \left(1 + \frac{r}{12}\right)^{24}
\]

### Step 3: Solve for $r$

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Here are 5 related questions:
1. How is monthly compounding different from yearly compounding in interest rate calculations?
2. What is the formula for continuously compounded interest?
3. How does increasing the number of compounding periods affect the final amount?
4. Can nominal and effective interest rates differ? Why?
5. What is the difference between simple interest and compound interest?

**Tip:** In compound interest problems, small differences in the interest rate can have a significant impact over long periods.

If an investment grew to $15,500 in 2 years and the interest amount earned was $950, calculate the nominal interest rate compounded monthly.

Learn how to calculate the nominal interest rate compounded monthly when an investment grows to $15,500 over 2 years with $950 in interest. This problem explores key financial mathematics concepts, including compound interest and exponential equations, suitable for students in Grades 11-12.

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