Find the value of an account into which $2327 is deposited at and APR of 6.70% compounding monthly for 6 years.  Round to the nearest penny.

To find the future value of the account after 6 years with monthly compounding, we use the compound interest formula:

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

Where:
- $ A $ is the future value of the investment/loan, including interest.
- $ P $ is the principal investment amount (initial deposit), which is \$2327.
- $ r $ is the annual interest rate (decimal), so $ r = 6.70\% = 0.067 $.
- $ n $ is the number of times the interest is compounded per year, which is 12 for monthly compounding.
- $ t $ is the time the money is invested for, in years, which is 6 years.

Now, let's plug the values into the formula:

\[
A = 2327 \left( 1 + \frac{0.067}{12} \right)^{12 \times 6}
\]

I'll calculate the future value.

The value of the account after 6 years, with monthly compounding at an APR of 6.70%, will be \$3474.54, rounded to the nearest penny.

Would you like further details or have any other questions?

Here are 5 related questions to explore further:
1. How would the future value change with a different interest rate?
2. What if the compounding was done quarterly instead of monthly?
3. How does the time period affect the future value in compound interest calculations?
4. What is the difference between simple interest and compound interest over the same period?
5. How does continuous compounding affect the future value compared to monthly compounding?

**Tip:** The more frequently the interest is compounded, the higher the final amount will be.

Find the value of an account into which $2327 is deposited at an APR of 6.70% compounding monthly for 6 years. Round to the nearest penny.

Learn how to calculate the future value of an account with $2327 deposited at an APR of 6.70%, compounding monthly for 6 years. This solution explains the compound interest formula and provides a step-by-step calculation, resulting in a future value of $3474.54. Ideal for students in Grades 10-12 studying exponential growth and compound interest.

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