Compound Interest Simulator

---
name: compound-interest-simulator
description: " and simulation and basis asset nature example tool. 'investment-advisor' and 'tax-strategist' agent investment revenue simulationand retirement specialist designto do when this skill's official, scenario comparison, retirement goal total must be utilized. ' total', 'asset nature example', 'retirement specialist simulation' etc. However, budget design tax total is outside this skill's scope."
---

# Compound Interest Simulator — simulator

 and simulation, asset nature example, retirement specialist total.

## core official

### daywhen 

```
FV = PV × (1 + r)^n

FV: un- value (Future Value)
PV: current value (Present Value)
r: annual revenuerate (number)
n: duration (year)

examplewhen: 1,0000,000 KRW annual 7% 30year investment
 FV = 1,000 only × (1.07)^30 = 7,6120,000 KRW
```

### basis quality (month)

```
FV = PMT × [(1 + r/12)^(12n) - 1] / (r/12)

PMT: month quality
r: annual revenuerate
n: duration (year)

examplewhen: month 500,000 KRW annual 7% 20year quality
 FV = 50 only × [(1.00583)^240 - 1] / 0.00583
 = 50 only × 520.9 = 200M 6,0450,000 KRW
 (KRW 100M 2,0000,000 KRW, revenue 100M 4,0450,000 KRW)
```

### retirement specialist (needed month quality)

```
PMT = FV × (r/12) / [(1 + r/12)^(12n) - 1]

examplewhen: 20year after 500M needed, annual 7% expectedrevenue
 PMT = 500M × 0.00583 / [(1.00583)^240 - 1]
 = 500M × 0.00192 = 95.90,000 KRW/month
```

## 72 (asset 2 duration)

```
asset 2 annualnumber ≈ 72 / annual revenuerate(%)

annual revenuerateby 2 duration:
 3%: 24year
 5%: 14.4year
 7%: 10.3year
 10%: 7.2year
 12%: 6year
 15%: 4.8year
```

## asset by expectedrevenuerate

| asset | annual expectedrevenuerate | nature(tablelevelgap) | nature |
|------|-------------|---------------|------|
| example/quality | 3-4% | 0% | KRW report, person less than |
|  | 3-5% | 3-5% | planquality, total |
| (company) | 4-7% | 5-8% | within revenue |
| week(within) | 7-10% | 15-20% | basis nature, |
| week | 7-10% | 14-18% | minute |
| week | 8-12% | 20-25% | nature·risk |
| department | 5-8% | 10-15% | dividend+whentaxgap |
| | 3-6% | 15-20% | person degree |

## scenario comparison simulation

### annual revenuerate gap impact (month 1000,000 KRW, 30year)

| annual revenuerate | total KRW | final asset | revenue | revenuerate(total) |
|----------|---------|----------|------|-----------|
| 3% | 3.600M | 5.800M | 2.200M | 61% |
| 5% | 3.600M | 8.300M | 4.700M | 131% |
| 7% | 3.600M | 12.200M | 8.600M | 239% |
| 10% | 3.600M | 22.600M | 19.000M | 528% |

### whenwork timing gap impact (month 500,000 KRW, annual 7%)

| whenwork | investment duration | KRW | final asset | notes |
|----------|----------|------|----------|------|
| 25tax | 35year | 2.100M | 10.800M | day whenwork |
| 30tax | 30year | 1.800M | 6.100M | 5year gap -4.700M |
| 35tax | 25year | 1.500M | 4.100M | |
| 40tax | 20year | 1.200M | 2.600M | |

## retirement design total

### retirement specialist needed calculation

```
month × 12 × retirement after duration(year) × person 

reportnumberquality total (person 3%, investmentrevenue 5%):
 actual revenuerate = 5% - 3% = 2%

25year retirement , month 3000,000 KRW needed when:
 needed specialist = 300 only × 12 / 0.02 × [1 - (1.02)^(-25)]
 ≈ 7.000M KRW

4% person rule (between):
 retirement specialist = annualbetween / 0.04
 = 3,6000,000 KRW / 0.04 = 9.000M KRW
```

### pension number reflected

```
done needed specialist = total needed specialist - pension current

pension expected number (2024 standard, 20year ):
 month pyeongbalanced 3000,000 KRW → month approx. 60-800,000 KRW
 month pyeongbalanced 5000,000 KRW → month approx. 100-1200,000 KRW

gap itemsperson assetas preparation
```

## simulation capability 

```markdown
## asset nature simulation

**initial investment**: X0,000 KRW | **month quality**: X0,000 KRW | **expected revenuerate**: X%
**investment duration**: Xyear

| annualgap | KRW total | asset value | revenue | revenuerate |
|------|----------|----------|------|--------|
| 5year | X0,000 KRW | X0,000 KRW | X0,000 KRW | X% |
| 10year | X0,000 KRW | X0,000 KRW | X0,000 KRW | X% |
| 15year | X0,000 KRW | X0,000 KRW | X0,000 KRW | X% |
| 20year | X0,000 KRW | X0,000 KRW | X0,000 KRW | X% |
| 30year | X0,000 KRW | X0,000 KRW | X0,000 KRW | X% |

**core insight**: [ and degree timing, tax savings utilization when addition and etc.]
```

## reference

- revenuerate un- reportdegree 
- detailed simulation model: `references/simulation-models.md` reference