# Investment Simulator

> Simulate how monthly investments grow over time with compound interest.

## What is this simulator?

The Investment Simulator is a powerful financial planning tool that models how regular monthly investments grow over time through the mechanism of compound interest. Compound interest — often called the eighth wonder of the world — means that your returns themselves generate additional returns, creating an exponential growth curve over long time horizons. This tool is particularly useful for anyone practicing dollar-cost averaging (DCA), a strategy where a fixed amount is invested at regular intervals regardless of market conditions. DCA is widely recommended by financial advisors because it removes the emotional element of trying to time the market and naturally results in buying more shares when prices are low and fewer when prices are high. The simulator visualizes the dramatic difference between your total invested principal and your projected final assets, making it an excellent motivational and educational resource. Whether you are saving for retirement, a down payment on a house, your children's education, or simply building long-term wealth, this simulator helps you set realistic expectations, compare different scenarios, and understand the critical role that time plays in wealth accumulation through compounding.

## How to use

Step 1: Enter your planned monthly investment amount. This should be a consistent sum you can comfortably invest each month without affecting your essential living expenses. Common starting amounts range from 100,000 KRW to 1,000,000 KRW per month, but any amount works.

Step 2: Set the investment period in years. Longer periods dramatically increase the compounding effect — even a difference of 5 years can result in tens of millions of won in additional returns. Consider your investment goal and timeline.

Step 3: Enter the expected annual return rate. Historical benchmarks include KOSPI at 8-10%, the S&P 500 at approximately 10%, and conservative bond portfolios at 3-5%. Be realistic rather than optimistic — using a range of scenarios (conservative, moderate, aggressive) gives you a better picture.

Step 4: Review the results. The calculator displays your expected final assets, total invested principal, total profit, and overall return rate. An interactive chart visualizes your asset growth year by year, clearly showing where compound interest begins to accelerate.

Tip: Try multiple scenarios by adjusting the monthly amount or return rate to see how small changes compound over decades.

## Formula

The simulator uses the future value of an annuity formula with monthly compounding:

FV = P × ((1 + r)^n - 1) / r

Where:
- FV = Future Value (total projected assets)
- P = Monthly investment amount
- r = Monthly interest rate (annual rate ÷ 12)
- n = Total number of months (years × 12)

Detailed Example:
Monthly investment: 500,000 KRW, Annual return: 8%, Period: 20 years
- r = 0.08 / 12 = 0.006667
- n = 20 × 12 = 240 months
- FV = 500,000 × ((1.006667)^240 - 1) / 0.006667
- FV ≈ 294,510,000 KRW
- Total invested = 500,000 × 240 = 120,000,000 KRW
- Total profit ≈ 174,510,000 KRW (145.4% return)

Comparison scenarios:
- Same amount at 5% for 20 years → ~205M KRW (profit: ~85M)
- Same amount at 8% for 30 years → ~745M KRW (profit: ~565M)
- 1,000,000/month at 8% for 20 years → ~589M KRW

Notice how extending from 20 to 30 years more than doubles the final value. This exponential growth is the essence of compound interest — the longer your money compounds, the faster it grows. The formula assumes reinvestment of all returns and a constant rate, which is a simplification of real market behavior but serves as an excellent planning baseline.

## Useful tips

Start early, even with small amounts. The single most important factor in compound growth is time. Someone who invests 300,000 KRW/month starting at age 25 will typically accumulate significantly more than someone investing 600,000 KRW/month starting at age 35, despite investing less total capital. This is because the earlier investor has 10 additional years of compounding.

Use conservative estimates for planning. While historical stock market returns average 8-10%, using 5-7% in your projections accounts for inflation, taxes, fees, and potential underperformance. It is better to be pleasantly surprised than disappointed.

Remember that this simulator shows pre-tax, pre-fee returns. In reality, you will pay capital gains tax on profits (currently 15.4% on dividends in Korea), fund management fees (typically 0.1-1.5% annually for ETFs/funds), and potentially securities transaction tax when selling. These costs can reduce effective returns by 1-3% annually.

Do not stop investing during market downturns. DCA works best when you maintain discipline through both bull and bear markets. Market dips actually benefit DCA investors because you purchase more shares at lower prices, reducing your average cost basis.

Consider inflation when interpreting results. A projected 300 million KRW in 30 years will have significantly less purchasing power than 300 million KRW today. At 2.5% annual inflation, 300M in 30 years is equivalent to roughly 143M in today's money.

Review and adjust your plan annually. As your income grows, try to increase your monthly investment amount. Even a 5-10% annual increase in contributions can dramatically improve long-term outcomes.

## FAQ

### Q. Is 8% annual return realistic?

The KOSPI index has historically delivered average annual returns of approximately 8-10% over multi-decade periods, and the S&P 500 has averaged around 10% since its inception. However, past performance does not guarantee future returns. Markets can experience extended periods of below-average returns, and individual years can vary dramatically from -40% to +50%. For conservative planning, many financial advisors recommend using 5-7% as your expected return, which accounts for potential underperformance and leaves room for positive surprises.

### Q. Are taxes and fees included in the simulation?

This simulator calculates gross (pre-tax, pre-fee) returns to provide a clean baseline projection. In practice, your actual returns will be reduced by several costs: dividend withholding tax of 15.4% in Korea, capital gains tax if applicable, fund management fees (typically 0.1-1.5% per year for ETFs and mutual funds), and securities transaction tax when selling. To approximate after-tax returns, consider reducing your expected annual return by 1-2 percentage points when inputting your rate.

### Q. What is the difference between DCA and lump-sum investing?

Dollar-Cost Averaging (DCA) involves investing a fixed amount at regular intervals (e.g., monthly), while lump-sum investing means deploying all available capital at once. Academic research shows that lump-sum investing outperforms DCA approximately two-thirds of the time because markets tend to rise over time, meaning earlier investment captures more growth. However, DCA significantly reduces the risk of investing a large sum at a market peak. DCA also has strong behavioral benefits — it automates the investment process and removes emotional decision-making, making it ideal for most individual investors.

### Q. How does inflation affect my projected returns?

Inflation erodes purchasing power over time, meaning that the projected future value in nominal terms will buy fewer goods and services than the same amount today. For example, at 2.5% average annual inflation over 20 years, 100 million KRW in future money is equivalent to approximately 61 million KRW in today's purchasing power. To account for this, you can either subtract the expected inflation rate from your nominal return (e.g., use 5.5% instead of 8% for a 'real' return estimate) or mentally discount your projected final value.

### Q. Can I change my monthly investment amount over time?

This simulator uses a fixed monthly amount for simplicity, but in reality, most investors increase their contributions as their income grows. If you plan to increase your monthly investment by, say, 5% each year, you can run multiple simulations with different amounts and periods to approximate your trajectory. For example, simulate the first 5 years at 500,000 KRW/month, then the next 5 years at 700,000 KRW/month, and add the results together for a more realistic long-term projection.