投资计算器

本投资计算器预测您的资金如何通过复利随时间增长。输入初始投资金额、每月定投金额、预期收益率和投资期限，查看总收益及详细的逐年增长明细。

Investment Calculator

Calculate the future value of your investment based on initial investment, regular contributions, interest rate, and time period.

常见问题

投资计算器是如何工作的？

投资计算器使用复利公式计算投资的未来价值：FV = PV × (1 + r)ⁿ，其中 PV 是本金，r 是期间收益率，n 是投资期数。如有定期追加投资，则额外使用年金公式计算。

复利频率如何影响投资收益？

复利频率越高，收益越大，但差异随复利次数增加而递减。年复利、月复利、日复利的年化有效收益率分别不同。连续复利公式为 FV = PV × e^(rt)，是理论上的最大值。

72 法则是什么？

72 法则是估算资金翻倍所需时间的简便方法：翻倍年数 ≈ 72 / 年收益率(%)。例如，年收益率 8%，则约 72/8 = 9 年资金翻倍。这是复利计算的快速估算工具。

通货膨胀如何影响投资收益？

通货膨胀会侵蚀投资的实际购买力。实际收益率 ≈ 名义收益率 - 通货膨胀率（精确公式：实际收益率 = (1 + 名义收益率) / (1 + 通胀率) - 1）。长期投资必须考虑通胀影响。

1. Investment Calculator Overview

What is an Investment Calculator?

An investment calculator is an essential financial planning tool that helps investors model and project their investment growth. This investment calculator specifically focuses on compound interest calculations, periodic investment contributions, and various compounding frequencies to provide accurate investment projections.

Investment Calculator Features

Investment Growth Projections: Calculate future investment values using advanced compound interest formulas for both lump sum and periodic investments
Investment Compounding Options: Model investment growth with various compounding frequencies including daily, weekly, monthly, quarterly, semi-annual, and annual compounding
Investment Contribution Analysis: Evaluate different investment scenarios with flexible contribution schedules and timing options
Investment Performance Visualization: View detailed investment growth charts and comprehensive investment analysis tables

2. Core Concepts and Calculations

Compound Interest Mechanism

Compound interest shows how returns are earned not only on your initial investment but also on previously accumulated returns. This powerful growth mechanism is expressed mathematically as:

FV = PV(1 + r)^n

Where: $FV$ = Future Value, $PV$ = Present Value, $r$ = Rate of Return, $n$ = Time Periods

Effective Annual Rate (EAR)

The Effective Annual Rate shows the actual annual return considering compounding effects:

i_{eff} = \left(1 + \frac{r}{m}\right)^m - 1

Where: $r$ = Nominal Interest Rate, $m$ = Number of Compounding Periods per Year

3. Formulas and Principles

Basic Formula

The fundamental formula for calculating the future value of a single lump-sum investment:

FV = PV\left(1 + \frac{r}{m}\right)^{mn}

Periodic Investment Formula

The formula to project future value when making regular contributions:

FV = PV\left(1 + \frac{r}{m}\right)^{mn} + PMT \times \frac{\left(1 + \frac{r}{m}\right)^{mn} - 1}{\frac{r}{m}}

Continuous Compounding

FV = PV \times e^{rn}

Where e is Euler's Number (approximately 2.71828)

Payment Timing Adjustment

For beginning-of-period investments:

FV_{advance} = FV_{arrears} \times \left(1 + \frac{r}{m}\right)

4. Important Considerations

Calculation Assumptions

Key Assumptions

Constant interest rate over the investment period
Regular contribution amounts remain unchanged
No withdrawals during the investment period
All returns are reinvested
No transaction costs or taxes are considered

Inflation Impact

Real\;Rate\;of\;Return = \frac{1 + Nominal\;Rate}{1 + Inflation\;Rate} - 1

Use real rates of return for more accurate long-term planning

5. Frequently Asked Questions

What return rate should I use?

Conservative portfolio (bonds heavy): 3-5% annual return
Balanced portfolio: 6-8% annual return
Aggressive portfolio (stocks heavy): 8-10% annual return
Historical market average: ~7% (inflation-adjusted)

How do I choose the compounding frequency?

Savings accounts: Daily or Monthly compounding
Bonds: Semi-annual compounding
Stock/ETF investments: Consider continuous compounding
CDs: Based on specific terms

6. Terms and Definitions

Present Value (PV): The initial investment amount.
Future Value (FV): The projected value of your investment at the end of the term.
Compounding Frequency ( $m$ ): The number of times per year that interest is calculated and added to the principal.
Periodic Payment ( $PMT$ ): The regular contribution amount made to an investment at specified intervals.
Investment Term ( $n$ ): The total time period over which an investment is held or analyzed.
Effective Annual Rate (EAR): The actual annual return when accounting for compounding frequency.