Ok I invest about 10k every year but increase the rate investment 30 percent by every 5th year and it goes on till 30 years so what will be total returns at 16 percent per annum if the cycle goes like I invest 10k every year for five years then increase the amount by 5 years and then increase the amount by 30 percent in next 5 years till 30 years 

Let's break down your investment scenario:

1. **Initial Investment:** You start with $10,000 per year for the first 5 years.
2. **Increased Investment:** After every 5 years, your annual investment increases by 30%.
3. **Annual Return Rate:** The investment grows at an annual return rate of 16%.
4. **Duration:** This continues for 30 years.

### Step-by-Step Calculation:

1. **Years 1-5:**
   - Investment per year = $10,000
   - Total investment = $10,000 × 5 = $50,000

2. **Years 6-10:**
   - Investment increases by 30%: $ 10,000 \times 1.3 = 13,000 $ per year.
   - Total investment = $13,000 × 5 = $65,000

3. **Years 11-15:**
   - Investment increases again by 30%: $ 13,000 \times 1.3 = 16,900 $ per year.
   - Total investment = $16,900 × 5 = $84,500

4. **Years 16-20:**
   - Investment increases again by 30%: $ 16,900 \times 1.3 = 21,970 $ per year.
   - Total investment = $21,970 × 5 = $109,850

5. **Years 21-25:**
   - Investment increases again by 30%: $ 21,970 \times 1.3 = 28,561 $ per year.
   - Total investment = $28,561 × 5 = $142,805

6. **Years 26-30:**
   - Investment increases again by 30%: $ 28,561 \times 1.3 = 37,129.30 $ per year.
   - Total investment = $37,129.30 × 5 = $185,646.50

### Final Computation:
To find the future value of each segment, we use the formula for the future value of a series of investments:

\[
\text{FV} = \text{Investment} \times \left[\frac{(1 + r)^n - 1}{r}\right] \times (1 + r)^{t-n}
\]

Where:
- $ r $ is the annual return rate (16% or 0.16)
- $ n $ is the number of years of investment
- $ t $ is the total time period the investment will grow

I'll now calculate the future value of each investment segment considering the time they will compound until the 30th year.

### Calculation in Detail:

I will compute these step by step.The total returns after 30 years, given your investment pattern and a 16% annual return rate, will be approximately **$6,962,109.24**.

This value accounts for the incremental increases in your annual investments every 5 years, with each segment compounded until the end of the 30-year period.

Would you like more details or have any questions? Here are some related questions to consider:

1. How does the total return change if the annual return rate is slightly different (e.g., 12% or 18%)?
2. What would be the impact on the total returns if the investment period was shorter, say 20 or 25 years?
3. How would the total returns differ if the investment increase was only 20% every 5 years?
4. What if you started with a different initial amount, like $5,000 or $15,000?
5. How does the total investment compare to the total return?

**Tip:** Regularly increasing your investment amount, even by a modest percentage, can have a substantial impact on your long-term returns due to the power of compounding.

Learn how to calculate total returns over 30 years with increasing annual investments and compound interest at 16% per annum. This detailed calculation considers incremental investment increases by 30% every 5 years. Discover the impact of compounding on long-term returns.

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