are you sure the answers aren't 1785.74 and 500.43?

Let's double-check the calculations. Here's a step-by-step recalculation to ensure the accuracy:

### Formula Recap:
1. **Present Value $ PV $**:
   \[
   PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}
   \]
2. **Compound Discount $ D $**:
   \[
   D = FV - PV
   \]

Given values:
- $ FV = 2298.17 $
- $ r = 0.031 $
- $ n = 4 $ (quarterly compounding)
- $ t = 8 $

Let me recompute that to see if we get different results.After recalculating, the present value is still approximately **$1795.12**, and the compound discount is **$503.05**. These results are accurate based on the formula and given inputs.

If your expectation was **$1785.74** and **$500.43**, it might be due to a different rounding method or a slight variation in the input values or interest calculation method (such as simple interest or a different compounding frequency). 

If you suspect an error or a different interpretation, I can help adjust the method or check further. Let me know how you'd like to proceed!

Explore a detailed step-by-step recalculation of present value and compound discount calculations in finance. Understand the formulas and inputs used, including a breakdown of calculations resulting in present value approximately $1795.12 and compound discount $503.05. Check if these match your expected values of $1785.74 and $500.43.

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