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Future ValueVarying the Period for a Present Value Calculation

The present value calculations on this page are applied to investments for which interest is compounded in each period of the investment.

However if you are supplied with a stated annual interest rate, and told that the interest is compounded monthly, you will need to convert the annual interest rate to a monthly interest rate and the number of periods into months:

monthly interest rate | = | annual interest rate / 12 |

number of months | = | number of years * 12 |

A similar conversion is required if interest is paid quarterly, semi-annually, etc.

For an example of this, see the section on How To Calculate Present Value When Interest is Compounded Monthly

If you want to calculate the present value of a single investment that earns a fixed interest rate, compounded over a specified number of periods, the formula for this is:

where,

- fv is the future value of the investment;
- rate is the interest rate per period (as a decimal or a percentage);
- nper is the number of periods over which the investment is made.

Present Value of a Single Cash Flow:

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

1 | Future Value: | 15000 |

2 | Annual Interest Rate: | 4% |

3 | Number of Years: | 5 |

4 | Present Value: | =15000/(1+4%)^5 |

For example, if you want a future value of $15,000 in 5 years' time from an investment which earns an annual interest rate of 4%, the present value of this investment (i.e. the amount you will need to invest) can be calculated by typing the following formula into any Excel cell:

=15000/(1+4%)^5

which gives the result *12328.9066*.

I.e. the present value of the investment (rounded to 2 decimal places) is *$12,328.91*.

As with all Excel formulas, instead of typing the numbers directly into the present value formula, you can use references to cells containing values. Therefore, the present value formula in cell B4 of the above spreadsheet could be entered as:

=B1/(1+B2)^B3

which returns the same result.

Instead of using the above formula, the present value of a single cash flow can be calculated using the built-in Excel PV function (which is generally used for a series of cash flows).

The syntax of the PV function is:

PV( rate, nper, [pmt], [fv], [type] )

where,

- rate is the interest rate per period (as a decimal or a percentage);
- nper is the number of periods over which the investment is made;
- [pmt] is the regular payment per period (if omitted, this is set to the default value 0);
- [fv] is the future value of the investment, at the end of nper payments (if omitted, this is set to the default value 0);
- [type] specifies whether the payment is made at the start or the end of the period.
This can have the value 0 or 1, meaning:

0 - the payment is made at the

__end__of the period (as for an__ordinary__annuity);

1 - the payment is made at the__start__of the period (as for an annuity__due__).If omitted, the [type] argument is set to the default value 0.

Note that, in line with the general cash flow sign convention, the PV function treats negative values as outflows and positive values as inflows.

Present Value of a Single Cash Flow:

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

1 | Future Value: | 15000 |

2 | Annual Interest Rate: | 4% |

3 | Number of Years: | 5 |

4 | Present Value: | =PV( 4%, 5, 0, 15000 ) |

For example, the above spreadsheet on the right shows the Excel PV function used to calculate the present value of an investment that earns an annual interest rate of 4% and has a future value of $15,000 after 5 years.

As shown in cell B4 of the spreadsheet, the PV function to calculate this is:

=PV( 4%, 5, 0, 15000 )

which gives the result *-$12,328.91*.

Note that in the above PV function:

- The [pmt] argument is set to 0, as there are no ongoing payments after the initial investment;
- The returned present value is negative, representing an
__outgoing__payment.

If the interest on your investment is compounded monthly (while being quoted as an __annual__ interest rate), the annual interest rate needs to be converted into a monthly interest rate and the number of years needs to be converted into months.

I.e.

monthly interest rate | = | annual interest rate / 12 |

number of months | = | number of years * 12 |

Present Value Formula With Interest Paid Monthly:

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

1 | Future Value: | 15000 |

2 | Annual Interest Rate: | 4% |

3 | Number of Years: | 5 |

4 | Present Value: | =PV( 4%/12, 5*12, 0, 15000 ) |

Therefore, if an investment has a stated annual interest rate of 4% (compounded monthly), and returns $15,000 after 5 years, the present value of the investment can be calculated as follows:

=PV( 4%/12, 5*12, 0, 15000 )

which returns the result *-$12,285.05*.

(Note that, once again, the value returned from the PV function is negative, representing an __outgoing__ payment).

If you want to calculate the present value of an annuity (a series of periodic constant cash flows that earn a fixed interest rate over a specified number of periods), this can be done using the Excel PV function.

The syntax of the PV function is:

PV( rate, nper, [pmt], [fv], [type] )

where,

- rate is the interest rate per period (as a decimal or a percentage);
- nper is the number of periods over which the investment is made;
- [pmt] is the regular payment per period (if omitted, this is set to the default value 0);
- [fv] is the future value of the investment, at the end of nper payments (if omitted, this is set to the default value 0);
- [type] specifies whether the payment is made at the start or the end of the period.
This can have the value 0 or 1, meaning:

0 - the payment is made at the

__end__of the period (as for an__ordinary__annuity);

1 - the payment is made at the__start__of the period (as for an annuity__due__).If omitted, the [type] argument is set to the default value 0.

Note that, in line with the general cash flow sign convention, the PV function treats negative values as outflows and positive values as inflows.

Present Value of a Series of Periodic Constant Cash Flows:

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

1 | Annual Interest Rate: | 4% |

2 | Number of Years: | 5 |

3 | Annual Payment: | 500 |

4 | Present Value: | =PV( 4%, 5, 500 ) |

For example, to calculate the present value of an ordinary annuity that has an annual interest rate of 4% and returns payments of $500 per year for 5 years, type the following formula into any Excel cell:

which gives the result *-$2,225.91*.

Note that in the above PV function:

- The [fv] argument is omitted, and so takes on the default value 0;
- the [type] argument is omitted, and so takes on the default value 0 (i.e. the calculation assumes that the payment is made at the
__end__of each year); - The returned present value is negative, representing an
__outgoing__payment.

Again, as with all Excel formulas, instead of typing the numbers directly into the present value formula, you can use references to cells containing values. Therefore, the PV function in cell B4 of the above spreadsheet could be entered as:

=PV( B1, B2, B3 )

which returns the same result.

A perpetuity is an annuity in which the constant periodic payments continue indefinitely.

The formula to calculate the present value of a perpetuity is:

=pmt/rate

where,

- pmt is the regular payment per period;
- rate is the interest rate per period (as a decimal or a percentage).

Present Value of a Perpetuity:

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

1 | Annual Payment: | 30000 |

2 | Annual Interest Rate: | 3.5% |

3 | Present Value: | =30000/3.5% |

For example, if you have a perpetuity that pays $30,000 per year and has an annual interest rate of 3.5%, the present value of the perpetuity can be calculated by typing the following formula into any Excel cell:

=30000/3.5%

This gives the result *857142.8571*.

I.e. the present value of the perpetuity (rounded to 2 decimal places) is *$857,142.86*.