Tyra invests $5400 in a new savings account which earns 4.3% annual interest, compounded daily.  What will be the value of her investment after 6 years?  Round to the nearest cent.

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

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

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 $5400 in this case).
- $ r $ is the annual interest rate (decimal) (4.3% or 0.043 in this case).
- $ n $ is the number of times that interest is compounded per year (365 for daily 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:

\[ P = 5400 \]
\[ r = 0.043 \]
\[ n = 365 \]
\[ t = 6 \]

Now, we plug these values into the formula:

\[ A = 5400 \left(1 + \frac{0.043}{365}\right)^{365 \cdot 6} \]

First, calculate the daily interest rate:

\[ \frac{0.043}{365} = 0.0001178 \]

Next, calculate the exponent:

\[ 365 \cdot 6 = 2190 \]

Now compute the value inside the parentheses:

\[ 1 + 0.0001178 = 1.0001178 \]

Raise this to the power of 2190:

\[ (1.0001178)^{2190} \approx 1.287178 \]

Finally, multiply this by the principal amount:

\[ A = 5400 \times 1.287178 \approx 6950.7612 \]

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

\[ A \approx \$6950.76 \]

So, the value of her investment after 6 years will be $6,950.76.

Would you like more details or have any questions?

Here are 8 related questions to explore further:
1. What if the interest rate were 5% instead of 4.3%? How would that affect the future value?
2. How would the future value change if the interest was compounded monthly instead of daily?
3. What would be the future value if Tyra invested for 10 years instead of 6?
4. How much interest would Tyra earn in total after 6 years?
5. How does continuous compounding affect the future value compared to daily compounding?
6. What is the impact of the principal amount on the future value of an investment?
7. How does the effective annual rate compare to the nominal annual rate in this scenario?
8. If Tyra made additional monthly contributions to the account, how would you calculate the future value?

**Tip:** When dealing with daily compounding interest, using a financial calculator or spreadsheet can simplify the calculations and help ensure accuracy.

Learn how to calculate the future value of a $5400 investment with daily compound interest at 4.3% annual interest rate over 6 years. Includes step-by-step solution using compound interest formula and daily compounding principles.

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