Calculate the proceeds of $5500 due in 7 years and 8 months discounted at 4.5%
compounded semi-annually.

To calculate the proceeds (also known as the present value) of $5500 due in 7 years and 8 months, discounted at 4.5% compounded semi-annually, we'll use the formula for the present value of a single sum:

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

Where:
- $ PV $ = Present Value (the proceeds)
- $ FV $ = Future Value ($5500)
- $ r $ = Annual nominal interest rate (4.5% or 0.045)
- $ n $ = Number of compounding periods per year (semi-annually, so $ n = 2 $)
- $ t $ = Time in years

### Step 1: Convert the time period into years
7 years and 8 months is equivalent to:

\[
t = 7 + \frac{8}{12} = 7 + \frac{2}{3} = 7.6667 \text{ years}
\]

### Step 2: Plug in the values into the formula
\[
PV = \frac{5500}{\left(1 + \frac{0.045}{2}\right)^{2 \times 7.6667}}
\]

### Step 3: Calculate the value
Let's calculate it step by step:

\[
PV = \frac{5500}{\left(1 + 0.0225\right)^{15.3334}} = \frac{5500}{(1.0225)^{15.3334}}
\]

\[
PV = \frac{5500}{1.3923} \approx 3,949.84
\]

So, the proceeds (present value) is approximately **$3,949.84**.

Would you like more details or have any questions?

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Here are five related questions:
1. How does the compounding frequency affect the present value calculation?
2. What would the proceeds be if the interest rate was compounded quarterly instead?
3. How would the present value change if the discount rate increased to 5%?
4. Can you calculate the future value if you invest $3,949.84 today at 4.5% for 7 years and 8 months?
5. What would be the impact of continuous compounding on the present value?

**Tip:** Always check the compounding frequency when dealing with present or future value calculations, as it significantly impacts the results.

Learn how to calculate the present value (proceeds) of $5500 due in 7 years and 8 months, discounted at 4.5% compounded semi-annually. Detailed step-by-step solution with the present value formula and calculations provided.

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