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The problem shown in the image asks how much more would be earned in the first investment compared to the second, given two different compounding situations:

1. **First Investment:**  
   - Principal: $48,000  
   - Rate: 10% compounded annually  
   - Time: 40 years  

2. **Second Investment:**  
   - Principal: $48,000  
   - Rate: 5% compounded monthly  
   - Time: 40 years  

The formula to calculate compound interest is:

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

Where:
- $A$ is the amount after interest.
- $P$ is the principal ($48,000).
- $r$ is the annual interest rate (expressed as a decimal, so 10% = 0.10 and 5% = 0.05).
- $n$ is the number of times the interest is compounded per year (for annual compounding, $n = 1$; for monthly compounding, $n = 12$).
- $t$ is the time in years (40 years).

Let me calculate both and find the difference.You would earn **$1,819,240** more on the first investment than on the second investment.

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:

1. How does changing the compounding frequency affect the total investment return?
2. What is the impact of the interest rate on long-term investments?
3. How would the results change if both investments were compounded annually?
4. What would happen if the time period for both investments was reduced to 20 years?
5. How can one calculate the effective annual rate for monthly compounding?

**Tip:** Always remember that more frequent compounding leads to a higher effective interest rate over time, even if the nominal rate remains the same.

How much more would you earn in the first investment than in the second investment? $48,000 invested for 40 years at 10% compounded annually vs. $48,000 invested for 40 years at 5% compounded monthly.

This problem explores two investments: $48,000 invested for 40 years at 10% compounded annually versus $48,000 invested for 40 years at 5% compounded monthly. Using the compound interest formula, calculate the total earnings and determine the difference between the two options.

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