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,
| 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:
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:
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:
where,
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.
| 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:
which gives the result -$12,328.91.
Note that in the above PV function:
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 |
| 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:
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:
where,
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.
| 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:
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:
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:
where,
| 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:
This gives the result 857142.8571.
I.e. the present value of the perpetuity (rounded to 2 decimal places) is $857,142.86.