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.
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 earing 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.)

To calculate how much the consumer has saved in their savings account, we can use the formula for compound interest, given that the account earns 2% annual interest compounded monthly.

The compound interest formula is:

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

Where:
- $A$ is the amount of money accumulated after $t$ years, including interest.
- $P$ is the principal amount (initial investment).
- $r$ is the annual interest rate (in decimal form).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the number of years.

In this case:
- $P = 7,500$ (the initial investment).
- $r = 0.02$ (2% annual interest).
- $n = 12$ (compounded monthly).
- $t = 6$ (the number of years the investment has been earning interest).

Now, let's calculate the amount of money in the savings account.

\[
A = 7500 \left(1 + \frac{0.02}{12}\right)^{12 \times 6}
\]

I'll calculate this.The consumer would have saved $8,455 in the savings account after 6 years, to the nearest dollar.

Would you like more details or have any other questions? Here are some related questions to think about:

1. How does compounding frequency affect the amount of interest earned?
2. What would the savings be with a different interest rate, say 3% APR?
3. How much more would the consumer need to save if the car's price increased by 5%?
4. If the savings were compounded annually instead of monthly, how much would the total savings differ?
5. How long would it take to save $10,000 at the current interest rate?

**Tip:** The more frequently interest is compounded, the more you benefit from earning "interest on interest."

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. 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 earing 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 compound interest using a savings account with 2% APR compounded monthly. This problem focuses on how a consumer's investment grows over 6 years to determine savings needed for a flying car purchase. Suitable for students in Grades 9-12.

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