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 problem, we need to find out how long it will take for Linda Baer's savings to grow from $3,280 to $7,388 at an interest rate of 7% compounded annually.

The formula to calculate the future value of an investment compounded annually is:

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

Where:
- $FV$ is the future value ($7,388),
- $PV$ is the present value ($3,280),
- $r$ is the annual interest rate (7% or 0.07),
- $n$ is the number of years.

We need to solve for $n$:

\[
7,388 = 3,280 \times (1 + 0.07)^n
\]

First, divide both sides of the equation by 3,280:

\[
\frac{7,388}{3,280} = (1.07)^n
\]

Now, simplify the left side:

\[
2.2537 = (1.07)^n
\]

Next, we take the natural logarithm (ln) of both sides to solve for $n$:

\[
\ln(2.2537) = n \times \ln(1.07)
\]

Finally, solve for $n$:

\[
n = \frac{\ln(2.2537)}{\ln(1.07)}
\]

Let's calculate the value of $n$.It will take Linda Baer approximately 12 years to save enough money to buy the car that costs $7,388, assuming her money is invested at 7% compounded annually.

Would you like more details or have any questions?

Here are five related questions:
1. What would be the future value after 10 years at the same interest rate?
2. How would the time change if the interest rate were compounded semi-annually?
3. What if Linda could save an additional $1,000 right now? How would that impact the timeline?
4. How long would it take if the interest rate increased to 8%?
5. What is the difference in savings time if Linda wanted to buy a car that costs $8,000 instead?

**Tip:** Always check if your interest rate is compounded annually, semi-annually, or quarterly, as this affects how much your money will grow over time.

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% compounded annually, how long will it take to buy a car that costs $7,388?

Find out how long it will take to save enough money to buy a car costing $7,388 if you start with $3,280 and invest it at 7% interest compounded annually. Learn about exponential growth and the future value formula. Ideal for high school students learning about compound interest.

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