### Calculating the Present and Future Values of a Single Sum

The future value (FV) calculation allows investors to predict, with a very high degree of accuracy, the amount of profit that can be generated by varying investments. The amount of growth earned by holding a given amount in cash will most likely be different than if that same amount were invested in stocks or other equities. The FV formula is used to compare multiple options and scenarios.

When applying the FV formula, the Present Value (PV) must first be calculated and then the rate and time period in which interest is earned, or compounded, is required to complete the calculation. As a result, the PV is multiplied times a constant of 1 plus the rate of return with an exponent of how many periods of interest is earned or compounded.

There is a formula for calculating future value.### Calculating Future Value Using Spreadsheets

Date | Investment | Future Value Formula | Future Value |
---|---|---|---|

Jan 1 − Age 19 | $2,400 | $=\$2{,}400\;(1+0.12)^1$ | $2,688.00 |

Jan 1 − Age 20 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$2{,}688\;(1+0.12)^1$ | $5,698.56 |

Jan 1 − Age 21 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$5{,}698.56\;(1+0.12)^1$ | $9,070.39 |

Jan 1 − Age 22 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$9{,}070.39\;(1+0.12)^1$ | $12,846.84 |

Jan 1 − Age 23 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$12{,}846.84\;(1+0.12)^1$ | $17,076.46 |

Jan 1 − Age 24 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$17{,}076.46\;(1+0.12)^1$ | $21,813.64 |

Jan 1 − Age 25 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$21{,}813.64\;(1+0.12)^1$ | $27,119.28 |

### Using Spreadsheets to Calculate Cumbersome Future Value Calculations

Date | Investment | Future Value Formula | Future Value |
---|---|---|---|

Jan 1 − Age 27 | $2,400 | $=\$2{,}400\;(1+0.12)^1$ | $2,688.00 |

Jan 1 − Age 28 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$2{,}688\;(1+0.12)^1$ | $5,698.56 |

Jan 1 − Age 29 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$5{,}698.56\;(1+0.12)^1$ | $9,070.39 |

Jan 1 − Age 30 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$9{,}070.39\;(1+0.12)^1$ | $12,846.84 |

Jan 1 − Age 31 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$12{,}846.84\;(1+0.12)^1$ | $17,076.46 |

Jan 1 − Age 32 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$17{,}076.46\;(1+0.12)^1$ | $21,813.64 |

[As time passes, the formula is the same each year.] | |||

Jan 1 − Age 64 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$1{,}461{,}193.28\;(1+0.12)^1$ | $1,639,224.47 |

Jan 1 − Age 65 | $2,400 | $=\$2{,}400\;(1+0.12)^1+\$1{,}639{,}224.47\;(1+0.12)^1$ | $1,838,619.41 |

### Calculating the Present and Future Values of an Annuity

Calculating the future value of an annuity can also be helpful. An **annuity** is a fixed, regular payment stream paid in the same amount over a period of time. This is similar to how Social Security monthly payments work. When retirement planning, some people want to know how much they need to save to invest in an annuity in order to have a guaranteed monthly income stream at some point in the future.

### Using Spreadsheets to Perform Financial Calculations

### Spreadsheet Functions

Formula Being Calculated | Spreadsheet Function | Calculator Key |
---|---|---|

Determine future value | FV (rate, nper, pmt, pv, type) |
FV |

Determine present value | PV (rate, nper, pmt, fv, type) |
PV |

Determine annuity payment | PMT (rate, nper, pv, fv, type) |
PMT |

### Spreadsheet File

A | B | C | |
---|---|---|---|

1 | Present Value | $500 | |

2 | # of Years | 5 | |

3 | APR | 0.08% | |

4 | Future Value | $735 | = FV (B3, B2, B1) |

*pv*,

*type*). Typing in the formula and then selecting the appropriate cells and hitting enter returns the result. By using a spreadsheet, Mary can easily see what the impact would be of a different annual rate, a different present value, or saving for more years. This can aid in the decision-making process by allowing Mary to substitute in different numbers and easily to try out different scenarios when making an investment decision.