Linda Baer has already saved ​$3 comma 280 to buy a used vehicle. Ignoring taxes and assuming her money is invested in a money market account earning 7 percent compounded​ annually, how long will it take to buy a car that costs ​$7 comma 388​?
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Ignoring taxes and assuming her money is invested in a money market account earning 7​% compounded​ annually, to save  the money to buy a car that costs ​$7 comma 388 will take

enter your response here years.  ​(Round to the nearest​ integer.)

To solve this, we use the formula for compound interest:

\[
FV = PV \times (1 + r)^t
\]

Where:
- $ FV $ is the future value (the amount she needs, which is $7,388),
- $ PV $ is the present value (the amount she has saved, which is $3,280),
- $ r $ is the annual interest rate (7%, or 0.07), and
- $ t $ is the time in years.

We need to solve for $ t $. The formula can be rearranged as:

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

Now, let's compute this.It will take approximately 12 years for Linda Baer to save enough money to buy a car that costs $7,388, assuming her money is invested at 7% compounded annually.

Would you like further details or have any other questions?

Here are 5 related questions you might find helpful:
1. What is the difference between simple interest and compound interest?
2. How does the frequency of compounding affect the final amount?
3. How do changes in the interest rate impact the time it takes to reach a financial goal?
4. Can Linda reduce the time needed by contributing additional savings? How?
5. How does inflation impact the real value of the amount saved?

**Tip:** When using compound interest, small changes in the interest rate can have a large impact on the final amount over long periods.

Linda Baer has already saved ​$3,280 to buy a used vehicle. Ignoring taxes and assuming her money is invested in a money market account earning 7 percent compounded annually, how long will it take to buy a car that costs ​$7,388?

Learn how to calculate the time needed to save for a car priced at $7,388 when starting with $3,280, using compound interest at an annual rate of 7%. This problem involves key concepts such as exponential growth, compound interest, and logarithmic equations. Suitable for high school students.

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