If 42,300 dollars is invested at an interest rate of 7
 percent per year, find the value of the investment at the end of 
5 years for the following compounding methods, to the nearest cent.

To calculate the future value of the investment, we can use the following formulas for each compounding method:

1. **Annual Compounding**:  
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount (initial investment).
- $ r $ is the annual interest rate (in decimal form).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the time the money is invested for, in years.

### Let's calculate the value of the investment for the following compounding methods:

1. **Annual Compounding**: $ n = 1 $
2. **Semiannual Compounding**: $ n = 2 $
3. **Quarterly Compounding**: $ n = 4 $
4. **Monthly Compounding**: $ n = 12 $
5. **Daily Compounding**: $ n = 365 $

Where:
- $ P = 42,300 $
- $ r = 7\% = 0.07 $
- $ t = 5 $ years

I'll calculate the value for each method now.The value of the investment at the end of 5 years, based on different compounding methods, is as follows:

1. **Annual Compounding**: \$59,327.94
2. **Semiannual Compounding**: \$59,668.33
3. **Quarterly Compounding**: \$59,845.12
4. **Monthly Compounding**: \$59,965.55
5. **Daily Compounding**: \$60,024.54

Would you like further details or have any questions?

Here are 5 related questions for you to explore:
1. How would the future value change if the interest rate were 6% instead of 7%?
2. What is the difference in future value between annual and daily compounding over 10 years?
3. How is continuous compounding different from daily compounding, and what would the future value be?
4. How does the principal amount impact the rate of growth with compound interest?
5. How can the formula for compound interest be derived from simple interest?

**Tip:** The more frequent the compounding period, the higher the future value of the investment.

If 42,300 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.

Discover how to calculate the future value of a $42,300 investment over 5 years at a 7% interest rate using different compounding methods. This guide provides a step-by-step solution using the compound interest formula and is suitable for students in Grades 10-12.

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