

If $850 was invested 8 months ago at a simple interest rate of 5.6%, what would be the value of the investment 14 months from now?


We can solve this by using the **simple interest formula**:

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

where:
- $A$ is the future value of the investment,
- $P$ is the principal (initial amount),
- $r$ is the annual interest rate (as a decimal),
- $t$ is the time in years.

### Step-by-Step Solution

1. **Principal (P):**
   - The initial investment was $850, so $P = 850$.

2. **Interest Rate (r):**
   - The interest rate is 5.6%, which we convert to a decimal: 
   \[
   r = \frac{5.6}{100} = 0.056
   \]

3. **Time (t):**
   - The investment period is from 8 months ago to 14 months from now, making the total time period $8 + 14 = 22$ months. Convert this into years:
   \[
   t = \frac{22}{12} = \frac{11}{6} \approx 1.833 \text{ years}.
   \]

4. **Calculate the future value (A):**
   Using the simple interest formula:
   \[
   A = 850 \left( 1 + (0.056 \times 1.833) \right)
   \]
   First, calculate the interest:
   \[
   0.056 \times 1.833 = 0.102648
   \]
   Now calculate the future value:
   \[
   A = 850 \times (1 + 0.102648) = 850 \times 1.102648 \approx 937.25
   \]

So, the value of the investment 14 months from now will be approximately **$937.25**.

Would you like more details or have any questions?

### Related Questions:
1. How does the future value change with a different interest rate?
2. What would be the value after 10 months instead of 14 months?
3. How does simple interest compare to compound interest for the same investment?
4. What would the future value be if the investment period was extended to 2 years?
5. How much interest is earned in just the first 8 months?

### Tip:
When dealing with time in interest calculations, always ensure the time unit (months or years) is consistent with the interest rate!

If $850 was invested 8 months ago at a simple interest rate of 5.6%, what would be the value of the investment 14 months from now?

Learn how to calculate the future value of an $850 investment with a simple interest rate of 5.6% over a period of 22 months. This step-by-step solution explains how to apply the simple interest formula and convert months to years for accurate interest calculation. Suitable for Grades 9-12.

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