Most people do not have the choice to drive or fly to a destination close to home but perhaps we will in the future. Two​ companies, one in Massachusetts and one in​ Slovakia, are working on producing a flying car. A prototype has entered the testing phase in Slovakia and the Massachusetts company is working on perfecting retractable wings on their car model. Although mass production has not​ begun, the prototypes have successfully reached lift off with ranges of just over 400 miles and speeds just over 100 miles per hour.
​Source: Marquis, E.​ "Aeromobil 2.5 flying car makes first flight​ test." AolAutos. 25 Oct 2013. Retrieved from​ http://translogic.aolautos.com/2013/10/25/aeromobil-2-5-flying-car-makes-first-test-flight/
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Part 1
Suppose the sticker price on a particular car was​ 17,090. A consumer expects to qualify for a rebate of​ $4,500 and receive an additional​ $3,500 for trading in his current car. Six years ago the consumer invested​ $7,500 in a savings account earning​ 2% APR compounded monthly. To the nearest dollar how much would the consumer have saved to purchase the​ car?
Total saved would be ​$
  
enter your response here.
​(Round to the nearest dollar as​ needed.)

To calculate how much the consumer would have saved in the savings account, we need to use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

where:
- $A$ is the amount of money saved after interest,
- $P = 7,500$ is the initial principal (the amount the consumer invested),
- $r = 0.02$ is the annual interest rate (2%),
- $n = 12$ is the number of times the interest is compounded per year (monthly compounding),
- $t = 6$ is the number of years the money was invested.

Let's calculate this.

\[
A = 7,500 \left(1 + \frac{0.02}{12}\right)^{12 \times 6}
\]The consumer would have saved $8,455 after six years in the savings account.

Would you like further details or have any other questions?

Here are five related questions:
1. How would the amount change if the interest rate was 3% instead of 2%?
2. What if the consumer had invested $10,000 instead of $7,500? How much would they have saved?
3. How does compounding frequency (monthly vs. yearly) affect the final amount?
4. How long would it take to double the investment with a 2% interest rate compounded monthly?
5. How would the savings change if the consumer made additional contributions each month?

**Tip:** Always check how often the interest compounds, as more frequent compounding will increase your total returns!

Suppose the sticker price on a particular car was​ $17,090. A consumer expects to qualify for a rebate of​ $4,500 and receive an additional​ $3,500 for trading in his current car. Six years ago the consumer invested​ $7,500 in a savings account earning​ 2% APR compounded monthly. To the nearest dollar how much would the consumer have saved to purchase the​ car? Total saved would be ​$ (Round to the nearest dollar as​ needed.)

Learn how to calculate the total amount saved using compound interest for a consumer's car purchase. This problem covers the compound interest formula, where $7,500 is invested at a 2% APR compounded monthly for 6 years. Suitable for high school students in Grades 10-12.

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