Capital on 1st October is 10,000 growing 8% daily. What will be the capital on 1st day of each next month and also on 31st December

To solve this problem, we'll calculate the capital for the 1st day of each subsequent month, as well as the capital on December 31st, assuming a growth rate of 8% daily.

### General Approach:
The capital on any day can be calculated using the formula for compound growth:
\[
C_n = C_0 \times (1 + r)^n
\]
Where:
- $C_n$ is the capital after $n$ days,
- $C_0$ is the initial capital,
- $r$ is the daily growth rate (in decimal form),
- $n$ is the number of days.

### Given:
- Initial capital ($C_0$) on 1st October = 10,000
- Daily growth rate ($r$) = 8% = 0.08

### Steps to Calculate Capital on the 1st of Each Month:

1. **1st November (31 days after 1st October)**:
   \[
   C_{31} = 10,000 \times (1 + 0.08)^{31}
   \]

2. **1st December (30 days after 1st November)**:
   \[
   C_{61} = 10,000 \times (1 + 0.08)^{61}
   \]

3. **1st January (31 days after 1st December)**:
   \[
   C_{92} = 10,000 \times (1 + 0.08)^{92}
   \]

4. **31st December (92 days after 1st October)**:
   \[
   C_{92} = 10,000 \times (1 + 0.08)^{92}
   \]

### Calculations:
Let me calculate these values.Here are the calculated capitals:

1. **1st November**: \$108,676.69
2. **1st December**: \$1,093,576.29
3. **1st January**: \$11,884,625.60
4. **31st December**: \$11,884,625.60

### Summary:
- The capital grows substantially due to the 8% daily increase, leading to a significant amount by the end of December.

Would you like more details or have any questions?

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Here are 5 related questions for further exploration:

1. How would the capital change if the growth rate was compounded monthly instead of daily?
2. What would the capital be on the 15th of each month?
3. How would a decrease in the daily growth rate to 5% affect the final capital on 31st December?
4. If the capital started at $5,000 instead, what would the capital be on the same dates?
5. How would the capital change if we included a withdrawal of $500 every month?

**Tip**: When dealing with exponential growth, small changes in the rate or time period can lead to large differences in the final amount.

Capital on 1st October is 10,000 growing 8% daily. What will be the capital on 1st day of each next month and also on 31st December?

Learn how to calculate the capital growth from an initial amount of $10,000 with an 8% daily increase. This example includes step-by-step calculations for the 1st of each subsequent month and the capital on December 31st. Suitable for Grades 10-12.

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