lumsum investment vs sip , with 12lacks calcuation after 10 yeras.

 

1. Lump Sum Investment:

For a lump sum, the total amount is invested at the beginning.

Formula:

$$A = P \times (1 + r)^t$$

Where:

• $P = 12,00,000$
• $r = 0.12$ (annual rate)
• $t = 10$

Calculation:

$$A = 12,00,000 \times (1 + 0.12)^{10}$$ $$A = 12,00,000 \times (1.12)^{10} \approx 12,00,000 \times 3.10585 = ₹37,26,993$$

---

2. Systematic Investment Plan (SIP):

For a SIP, ₹10,000 is invested monthly for 10 years.

Formula:

$$FV = P \times \frac{(1 + r)^n - 1}{r} \times (1 + r)$$

Where:

• $P = 10,000$ (monthly investment)
• $r = 0.12 / 12 = 0.01$ (monthly return rate)
• $n = 10 \times 12 = 120$ (number of months)

Calculation:

$$FV = 10,000 \times \frac{(1 + 0.01)^{120} - 1}{0.01} \times (1 + 0.01)$$ $$FV = 10,000 \times \frac{(1.01)^{120} - 1}{0.01} \times 1.01$$ $$(1.01)^{120} \approx 3.30039$$ $$FV = 10,000 \times \frac{3.30039 - 1}{0.01} \times 1.01$$ $$FV = 10,000 \times 230.039 \times 1.01 \approx ₹23,33,433$$

---

Comparison of Results:

1. Lump Sum Investment: ₹37,26,993
2. SIP Investment: ₹23,33,433

---

Why the Difference?

• The lump sum investment benefits from compounding over the entire 10 years.
• In SIP, investments are spread over time, so only the earlier contributions compound for a longer period, resulting in a lower final amount.

Would you like to explore any specific scenarios or optimize your investment plan?

You said:

in above case, how does our amount become compounding, how does it crosses inflation of every year 8-9%? using general rune 8-4-3, how does mutual investment grow ?

ChatGPT said:

Understanding Compounding and Inflation in Investment Growth:

Compounding in Investments:

Compounding grows your investment by reinvesting the returns, creating a "snowball effect." Over time, your returns also start earning returns, which accelerates growth.

Impact of Inflation:

Inflation erodes the purchasing power of money, meaning your investment must grow faster than the inflation rate to provide real gains.

For example:

• Inflation Rate: 8% per year
• Investment Return: 12% per year
• Real Return (adjusted for inflation): $12\% - 8\% = 4\%$

---

General Rule 8-4-3 for Mutual Fund Growth:

This rule explains how investments grow based on three parameters:

1. 8% Rule: Average inflation rate in developing economies like India.
2. 4% Real Return: The return after subtracting inflation (12% return - 8% inflation).
3. 3% Net Real Return: If taxes, fund management fees, or other costs consume an additional 1%, you may retain a 3% net return.

---

How Does Mutual Fund Investment Grow?

1. Growth Formula:

   $$\text{Real Value} = \text{Future Value} / (1 + \text{Inflation Rate})^t$$

2. Example for ₹12,00,000 (Lump Sum Investment):

   • Investment Growth: ₹37,26,993 (after 10 years at 12% return).
   • Inflation Adjustment: With 8% annual inflation: $$\text{Real Value} = \frac{37,26,993}{(1 + 0.08)^{10}} = \frac{37,26,993}{2.1589} \approx ₹17,26,312$$
     • The purchasing power of ₹37,26,993 in 10 years is equivalent to ₹17,26,312 today.

3. Net Growth After Inflation:

   • Initial Investment = ₹12,00,000
   • Real Value After 10 Years = ₹17,26,312
   • Net Real Growth: $$\text{Net Growth} = ₹17,26,312 - ₹12,00,000 = ₹5,26,312$$
   • The investment beats inflation, offering significant real returns.

---

How Does Mutual Fund Growth Compensate for Inflation?

Mutual funds grow through:

1. Equity Exposure: Provides higher returns (12%-15%) compared to inflation.
2. Compounding: Longer durations amplify the effects of reinvested returns.
3. Diversification: Reduces risk and enhances stability of returns.

Why Mutual Funds Beat Inflation:

• Example: Parag Parikh Flexi Cap Fund:
  • Average annual return: 14% over the past 10 years.
  • Real Return After Inflation: $14\% - 8\% = 6\%$, which compounds over time.

---

Illustrative Table for Mutual Fund Growth vs. Inflation

Year	Investment Value (12%)	Inflation Value (8%)	Real Value
0	₹12,00,000	₹12,00,000	₹12,00,000
5	₹21,31,441	₹17,63,915	₹12,08,360
10	₹37,26,993	₹31,84,212	₹17,26,312

---

Conclusion:

• Mutual Funds Beat Inflation: With returns > inflation, mutual funds grow wealth effectively.
• Compounding Helps Long-Term Investors: The longer you stay invested, the more compounding offsets inflation.

Would you like further assistance in selecting funds or projecting your investments?