**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 of a sum of money. The present value (PV) is the amount you need to invest now to achieve a future value (FV) given a certain interest rate and time period. The formula is:

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

Where:
- $FV$ is the future value, which is $10,300.
- $r$ is the annual interest rate, which is 8% or 0.08.
- $t$ is the time period, which is 8 years.

Now, let's substitute the values into the formula:

\[
PV = \frac{10,300}{(1 + 0.08)^8}
\]

\[
PV = \frac{10,300}{(1.08)^8}
\]

\[
PV = \frac{10,300}{1.85093} \approx 5,565.17
\]

So, you would need to set aside approximately **$5,565.17** now to provide $10,300 in 8 years at an interest rate of 8%.

Do you want further details on how this calculation works or have any other questions?

Here are 5 related questions you may want to explore:
1. How does the present value change with different interest rates?
2. What is the future value if you invest $5,565.17 at 8% for 8 years?
3. How do compounding frequencies affect the present value calculation?
4. What if the interest is compounded monthly instead of annually?
5. How much would you need to invest for a 10-year period instead of 8 years?

**Tip**: When dealing with interest rates and time periods, be mindful of how frequently the interest is compounded, as this can significantly affect 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?

Learn how to calculate the present value of $10,300 over 8 years with an interest rate of 8%. This problem introduces key finance concepts like the present value formula and compound interest. The step-by-step guide is suitable for high school students, Grades 10-12.

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