You’re trying to save to buy a new $255,000 Ferrari. You have $44,000 today that can be invested at your bank. The bank pays 5.1 percent annual interest on its accounts. How long will it be before you have enough to buy the car?

To determine how long it will take to save enough to buy the Ferrari, we can use the formula for compound interest:

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

Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest (which is $255,000 in this case).
- $ P $ is the principal amount (the initial amount of money, which is $44,000).
- $ r $ is the annual interest rate (which is 5.1% or 0.051).
- $ n $ is the number of times that interest is compounded per year (assuming the interest is compounded annually, $ n = 1 $).
- $ t $ is the number of years the money is invested.

Since we are solving for $ t $, we need to rearrange the formula:

\[
t = \frac{\log\left(\frac{A}{P}\right)}{n \cdot \log\left(1 + \frac{r}{n}\right)}
\]

Plugging in the values:

\[
t = \frac{\log\left(\frac{255,000}{44,000}\right)}{\log\left(1 + 0.051\right)}
\]

Let me calculate that for you.It will take approximately **35.32 years** to save enough money to buy the $255,000 Ferrari, assuming you invest $44,000 today at an annual interest rate of 5.1%.

Would you like more details on the calculation or have any questions?

Here are some related questions you might find interesting:
1. What happens if the interest rate increases to 6%?
2. How much more will you need to invest initially to reduce the time by 5 years?
3. What if the bank compounds interest quarterly instead of annually?
4. How much will you have after 20 years if you keep the money invested at 5.1%?
5. What if you decide to save $10,000 more after 10 years? How will that affect the timeline?

**Tip:** When planning long-term investments, always consider the impact of compound interest and how changes in the interest rate can significantly affect your savings goals.

Learn how long it will take to save enough money to buy a $255,000 Ferrari using compound interest calculations. This problem involves the compound interest formula and exponential growth concepts, assuming an initial investment of $44,000 at a 5.1% annual interest rate. Suitable for high school students.

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