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**Calculate the Inflation-Adjusted, After-Tax Future Value of a Single Deposit**
# Future Value of Investment

## Future Value Formula

### Formula Terms / Definitions

## Future Value After Taxes

### Formula Terms / Definitions

### 2018 United States Income Tax Rates

#### Standard Deduction

### 2018 Capital Gains Taxes

## Future Value After Taxes & Inflation

### Formula Terms / Definitions

## Continuous Compounding Interest Formula

### Formula Terms / Definitions

This calculator will help you to determine the after-tax future value of a lump-sum investment in today's dollars. Enter the amount invested, your anticipated investment APR, the anticipated rate of inflation along with the rate the investment will be taxed at to see how much money you'll have saved in the future along with what that money would be worth in today's dollars. If you do not want to account for taxes or inflation you can set those inputs to zero.

The results will show how various compounding frequencies on the investment impact the overall returns, along with the returns after taxes are paid & inflation is taken into account.

The above tabs allow you to switch between the calculator and current market rates available on high yield savings accounts & CDs of various durations including 1, 3, 6 & 9 months along with 1, 2, 3 and 5 year terms.

The basic formula for future value is as follows:

FV = PV * (1 + r)^{n}

- FV: future value
- PV: present value
- r: rate of return, expressed as a decimal rather than percent (percent divided by 100)
- n: number of compounding periods

That formula will give you the future value of an investment in nominal terms, however it does not adjust the results for inflation or the impact of taxes.

To account for taxes would start with the same formula

FV = PV * (1 + r)^{n}

but then subtract the taxes from the gains.

FVaftertaxes = ((PV * (1 + r)^{n}) - PV) * (1 - tr) + PV

- FVaftertaxes: future value, after accounting for the impact of taxes
- PV: present value
- r: rate of return, expressed as a decimal rather than percent (percent divided by 100)
- n: number of compounding periods
- tr: tax rate on investment, as expressed as a deciminal rather than a percent (percent divided by 100)

It is worth noting the above presumes the investment is taxed at the end of the investment period rather than taxed throughout the period. This in turn allows some of the gains to compound before taxing. If returns were taxed each year then the formula would need to be changed to subtract tax after each compounding cycle rather than doing it at the end.

Long term capital gains are typically taxed at a signficantly lower rate than short term capital gains. Short term gains are typically taxed similarly to ordinary income.

Rate | For Unmarried Individuals, Taxable Income Over | For Married Individuals Filing Joint Returns, Taxable Income Over | For Heads of Households, Taxable Income Over |
---|---|---|---|

10% | $0 | $0 | $0 |

12% | $9,525 | $19,050 | $13,600 |

22% | $38,700 | $77,400 | $51,800 |

24% | $82,500 | $165,000 | $82,500 |

32% | $157,500 | $315,000 | $157,500 |

35% | $200,000 | $400,000 | $200,000 |

37% | $500,000 | $600,000 | $500,000 |

Filing Status | Deduction Amount |
---|---|

Single | $12,000 |

Married Filing Jointly | $24,000 |

Head of Household | $18,000 |

Interest on a normal savings account is taxed annually. Banks typically issue a 1099-INT in the first month of the following calendar year.

Ordinary annuity returns are taxed when the money is withdrawn. If an annuity is purchased using pre-tax money then the entire balance is taxable, with taxes applying to each traunch that is withdrawn. If the purchase was made using after-tax funds then only the earnings are taxable, and the principal portion of each payment is not taxed. If a deferred annuity is cashed out via a lump sum then income tax will be due on all earnings above the original investment amount.

Short-term capital gains - which are typically assessed on investments held under 1 year - are taxed as ordinary income.

Long-Term Capital Gains Rate | Single Taxpayers | Married Filing Jointly | Head of Household | Married Filing Separately |
---|---|---|---|---|

0% | Up to $38,600 | Up to $77,200 | Up to $51,700 | Up to $38,600 |

15% | $38,600-$425,800 | $77,200-$479,000 | $51,700-$452,400 | $38,600-$239,500 |

20% | Over $425,800 | Over $479,000 | Over $452,400 | Over $239,500 |

Both short-term and long-term capital gains are also assessed an additional 3.8% net investment income tax for high earners. The 3.8% assessment was part of the Affordable Care Act, which has yet to be repealed.

Nominal dollars are not the same thing as actual spending power. Our debt-based fractional reserve monetary system is inherently inflationary, which means the value of currency generally declines over time.

To account for the decline in purchasing power we must subtract the compounded impacts of inflation from the final total.

FVafterttaxandinflation = (((PV * (1 + r)^{n}) - PV) * (1 - tr) + PV) * (1 - ir)^{n}

- FVafterttaxandinflation: future value, after subtracting tax payments & then accounting for the impacts of inflation
- PV: present value
- r: rate of return, expressed as a decimal rather than percent (percent divided by 100)
- n: number of compounding periods
- tr: tax rate on investment, as expressed as a deciminal rather than a percent (percent divided by 100)
- ir: rate of inflation, as expressed as a deciminal rather than a percent (percent divided by 100)

The above calculations are quite easy to do for interest or returns which compound annually. For investments which compound many times per year you have to divide the rate of return by the number of times the investment compounds each year & then multiply the annual periods by the number of times the investment compounds per year.

For continuously compounding interest the mathematical constant *e* is used.

FV = PV * *e*^{r n}

- FV: future value
- PV: present value
*e*: mathematical constant*e*, also known as Euler's number, which is approximately equal to 2.71828- r: rate of return, expressed as a decimal rather than percent (percent divided by 100)
- n: number of compounding periods