5
Your parents agree to pay half of the purchase price of a new car when you graduate from college. You will graduate and buy the car two years from now. You have $6,000 to invest today and can earn 10% on invested funds. What is the maximum you can spend on the new car with your parents' financial assistance?

To determine the maximum amount you can spend on a new car with your parents' assistance, we need to calculate the future value of your current investment and then combine it with your parents' contribution.

### Steps to Solve

1. **Calculate the Future Value of Your Investment:**

   You have $6,000 to invest today at an interest rate of 10% per year. The future value (FV) of this investment after 2 years can be calculated using the formula for compound interest:

   \[
   \text{FV} = P \times (1 + r)^n
   \]

   Where:
   - $ P $ is the principal amount ($6,000).
   - $ r $ is the annual interest rate (10% or 0.10).
   - $ n $ is the number of years (2).

   Substituting the values, we get:

   \[
   \text{FV} = 6000 \times (1 + 0.10)^2 = 6000 \times (1.10)^2
   \]

2. **Calculate Your Total Contribution:**

   Your parents agree to pay half of the purchase price of the car. This means that the future value of your investment will constitute half of the total purchase price. Let's calculate the total purchase price ($ C $):

   \[
   \text{Your Contribution} = \frac{C}{2} = \text{FV}
   \]

   So,

   \[
   C = 2 \times \text{FV}
   \]

3. **Substitute FV to Find C:**

   Now, let's plug in the future value to find out the total purchase price:

   \[
   \text{FV} = 6000 \times (1.10)^2 = 6000 \times 1.21 = 7260
   \]

   Therefore, the total cost of the car will be:

   \[
   C = 2 \times 7260 = 14520
   \]

### Conclusion

The maximum amount you can spend on the new car, including your parents' contribution, is **$14,520**.

### Would you like to know more?

If you have any further questions or need additional clarification, feel free to ask!

### Relative Questions

1. How is compound interest different from simple interest?
2. What would the future value be if the interest rate were 8% instead of 10%?
3. How does the investment period affect the future value of an investment?
4. Can you calculate the future value if the compounding period is semi-annual?
5. How do you calculate the future value if you make additional contributions to the investment each year?
6. What if your parents only agreed to pay a third of the car's price instead of half?
7. What happens to the future value if the interest rate is compounded monthly instead of annually?
8. How can you determine the required present value to reach a specific future value?

### Tip

When investing, always consider the effect of compounding frequency, as it can significantly impact the future value of your investment.

Learn how to calculate the maximum amount you can spend on a new car using compound interest and future value calculation. This problem involves investing $6,000 at 10% interest for 2 years to determine the total car purchase cost with parental assistance. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation