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The image shows a problem asking for the **present value** of a future sum of **$1,250.00** due at different time intervals (0.5, 1, 2, and 3 years) and varying interest rates (10% and 12%).

To find the present value (PV), we use the **Present Value formula**:

\[
PV = \frac{FV}{(1 + r)^n}
\]

Where:
- $ PV $ = Present Value
- $ FV $ = Future Value (\$1,250 in this case)
- $ r $ = Interest rate (given as 10% or 12%)
- $ n $ = Number of periods (in years: 0.5, 1, 2, 3)

Here are the steps to solve for each combination:

1. **At 10% for 0.5 years**:
   \[
   PV = \frac{1250}{(1 + 0.10)^{0.5}}
   \]

2. **At 10% for 1 year**:
   \[
   PV = \frac{1250}{(1 + 0.10)^1}
   \]

3. **At 10% for 2 years**:
   \[
   PV = \frac{1250}{(1 + 0.10)^2}
   \]

4. **At 10% for 3 years**:
   \[
   PV = \frac{1250}{(1 + 0.10)^3}
   \]

5. **At 12% for 0.5 years**:
   \[
   PV = \frac{1250}{(1 + 0.12)^{0.5}}
   \]

6. **At 12% for 1 year**:
   \[
   PV = \frac{1250}{(1 + 0.12)^1}
   \]

7. **At 12% for 2 years**:
   \[
   PV = \frac{1250}{(1 + 0.12)^2}
   \]

8. **At 12% for 3 years**:
   \[
   PV = \frac{1250}{(1 + 0.12)^3}
   \]

I will now compute these values.Here are the computed present values for the given future sum of $1,250 at different interest rates and time periods:

1. **At 10% interest**:
   - For 0.5 years: $ PV = 1191.83 $
   - For 1 year: $ PV = 1136.36 $
   - For 2 years: $ PV = 1033.06 $
   - For 3 years: $ PV = 939.14 $

2. **At 12% interest**:
   - For 0.5 years: $ PV = 1181.14 $
   - For 1 year: $ PV = 1116.07 $
   - For 2 years: $ PV = 996.49 $
   - For 3 years: $ PV = 889.73 $

Let me know if you'd like more details or have any questions!

Here are some related questions:
1. How does increasing the interest rate affect the present value?
2. What happens to the present value when the time period increases?
3. How would the formula change if the interest was compounded monthly instead of annually?
4. What is the future value if you know the present value and want to solve in reverse?
5. How does a higher present value affect investment decisions?

**Tip**: The longer the period or the higher the interest rate, the lower the present value.

Calculate the present value of $1,250 due at the end of different time periods (0.5 years, 1 year, 2 years, and 3 years) at varying interest rates of 10% and 12%.

Learn how to calculate the present value of $1,250 due at different time periods (0.5, 1, 2, and 3 years) with interest rates of 10% and 12%. This guide walks through the step-by-step process using the present value formula and covers key financial concepts like the time value of money.

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