**a.** The cost of a new automobile is $10,300. If the interest rate is 8%, how much would you have to set aside now to provide this sum in eight years?

To solve this problem, we will use the formula for the present value (PV) of a future sum, which is derived from the formula for compound interest:

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

Where:
- $FV$ is the future value (in this case, $10,300),
- $r$ is the annual interest rate (8%, or 0.08 as a decimal),
- $n$ is the number of years (8 years).

### Step-by-step Calculation:
\[
PV = \frac{10,300}{(1 + 0.08)^8}
\]

First, calculate $ (1 + 0.08)^8 $:
\[
(1 + 0.08)^8 = 1.08^8 \approx 1.85093
\]

Now, divide the future value by this amount:
\[
PV = \frac{10,300}{1.85093} \approx 5,565.49
\]

### Conclusion:
You would need to set aside approximately **$5,565.49** now to have $10,300 in 8 years at an 8% interest rate.

Would you like further details or clarifications on any part of this solution?

Here are some related questions you might find interesting:
1. How does compound interest affect long-term savings?
2. How would the amount change if the interest rate were lower?
3. What happens if the interest is compounded monthly instead of annually?
4. How can you calculate interest for different time periods (e.g., quarterly)?
5. How do you calculate future value if the present value and interest rate are known?

**Tip:** When dealing with compound interest, the time period (years, months, etc.) and the frequency of compounding (annually, monthly, etc.) have significant impacts on the result.

The cost of a new automobile is $10,300. If the interest rate is 8%, how much would you have to set aside now to provide this sum in eight years?

Discover how to calculate the present value needed to reach $10,300 in 8 years at an 8% interest rate. Using the present value formula, we break down the compound interest process step-by-step, perfect for high school students learning financial math.

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