you have decided to invest $12 000 for 6 years and you have a choice between two accounts. The first pays 7% per year, compounded monthly. The second pays 6.8% per year, compounded continuously. which one is better investement?

To determine which investment is better, we need to calculate the future value of both accounts after 6 years and compare them.

### Account 1: 7% per year, compounded monthly
For this account, we use the compound interest formula:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where:
- $A$ is the future value of the investment,
- $P$ is the initial principal (investment amount),
- $r$ is the annual interest rate (as a decimal),
- $n$ is the number of times the interest is compounded per year,
- $t$ is the number of years.

For this account:
- $P = 12,000$,
- $r = 0.07$,
- $n = 12$ (since it's compounded monthly),
- $t = 6$.

Now, let's calculate the future value $A$.

### Account 2: 6.8% per year, compounded continuously
For this account, we use the continuous compound interest formula:
\[
A = P \cdot e^{rt}
\]
where:
- $A$ is the future value of the investment,
- $P$ is the initial principal,
- $r$ is the annual interest rate (as a decimal),
- $t$ is the number of years,
- $e$ is Euler's number (approximately 2.71828).

For this account:
- $P = 12,000$,
- $r = 0.068$,
- $t = 6$.

Now, let's calculate the future value $A$ for both accounts.After 6 years:

- The future value of the first account (7% compounded monthly) is **$18,241.27**.
- The future value of the second account (6.8% compounded continuously) is **$18,045.69**.

Therefore, the **first account** (7% compounded monthly) is the better investment, as it yields a higher future value.

Would you like further details on the calculations or have any other questions?

Here are 5 related questions:
1. How would the results change if both accounts had the same interest rate but different compounding periods?
2. What would happen if the investment period was extended to 10 years?
3. How does continuous compounding generally compare to monthly compounding?
4. How much would need to be invested in each account to reach $25,000 in 6 years?
5. What is the difference in total interest earned between the two accounts?

**Tip:** The more frequently interest is compounded, the higher the future value, all other factors being equal.

You have decided to invest $12,000 for 6 years, and you have a choice between two accounts. The first pays 7% per year, compounded monthly. The second pays 6.8% per year, compounded continuously. Which one is the better investment?

This article compares two investment options: one offering 7% compounded monthly and the other 6.8% compounded continuously. Using the compound interest and continuous compounding formulas, we determine which account yields a higher return after 6 years. Suitable for students in Grades 11-12 and those learning about exponential growth.

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