Eva invests $7900 in a new savings account which earns 5.0% annual interest, compounded monthly.  What will be the value of her investment after 6 years?  Round to the nearest cent.

To calculate the future value of Eva's investment in a savings account with interest compounded monthly, we use the formula for compound interest:

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

Where:
- $ A $ is the amount of money accumulated after $ n $ years, including interest.
- $ P $ is the principal amount (the initial amount of money, which is $7900 in this case).
- $ r $ is the annual interest rate (decimal) (5.0% or 0.05 in this case).
- $ n $ is the number of times that interest is compounded per year (12 for monthly compounding).
- $ t $ is the time the money is invested for in years (6 years in this case).

Let's substitute the given values into the formula:

\[ P = 7900 \]
\[ r = 0.05 \]
\[ n = 12 \]
\[ t = 6 \]

Now, we plug these values into the formula:

\[ A = 7900 \left(1 + \frac{0.05}{12}\right)^{12 \cdot 6} \]

First, calculate the monthly interest rate:

\[ \frac{0.05}{12} = 0.0041667 \]

Next, calculate the exponent:

\[ 12 \cdot 6 = 72 \]

Now compute the value inside the parentheses:

\[ 1 + 0.0041667 = 1.0041667 \]

Raise this to the power of 72:

\[ (1.0041667)^{72} \approx 1.34885 \]

Finally, multiply this by the principal amount:

\[ A = 7900 \times 1.34885 \approx 10656.915 \]

Rounded to the nearest cent, the value of Eva's investment after 6 years will be:

\[ A \approx \$10656.92 \]

So, the value of her investment after 6 years will be $10,656.92.

Would you like more details or have any questions?

Here are 8 related questions to explore further:
1. What if the interest rate were 6% instead of 5%? How would that affect the future value?
2. How would the future value change if the interest was compounded quarterly instead of monthly?
3. What would be the future value if Eva invested for 10 years instead of 6?
4. How much interest would Eva earn in total after 6 years?
5. How does continuous compounding affect the future value compared to monthly compounding?
6. What is the formula for compound interest, and how is it derived?
7. How does the frequency of compounding impact the effective annual rate?
8. If Eva makes additional monthly contributions to the account, how would you calculate the future value?

**Tip:** When calculating compound interest, more frequent compounding periods (like monthly or daily) will result in a higher future value compared to less frequent compounding periods (like annually or quarterly).

Learn how to calculate compound interest with monthly compounding for Eva's savings account. Eva invests $7900 at an annual interest rate of 5.0%, compounded monthly, for 6 years. Find out the future value of her investment rounded to the nearest cent. Includes step-by-step calculation and related questions.

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