The PV function calculates the net present value for an investment or loan. PV stands for present value.
1. PV Function Syntax
PV(rate, nper, pmt, [fv], [type])
2. PV Function Arguments
| rate |
Required. The interest rate per period. If nper is years then the interest rate is per year. Divide the interest rate with 12 if you use months in the nper argument. |
| nper |
Required. The total number of payment periods in an annuity. |
| pmt |
Required. The payment amount per period. Interest and principal is often included in this amount but not other fees or taxes. The pmt argument is not used if you use the [fv] argument. |
| [fv] |
Optional. The future value. |
| [type] |
Optional. The number 0 or 1 and indicates when payments are due. |
3. PV Function example
Formula in cell C7:
=PV(C3, C4, C5)
4. What is the formula behind the PV function?
Formula:
(-pmt(1+rate*type)*(((1+rate^nper)-1)/rate)-fv)/((1+rate)^nper)
Formula in cell C7:
=-(C5*(1+C3*0)*(((1+C3)^C4-1)/C3)/((1+C3)^C4))
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5. How is the result of the PV function calculated in detail?
The PV function in cell C6 calculates the present value of an annuity loan or the amount you can borrow when the interest rate is 5% per year and the loan is paid back in ten years. In other words, it calculates how much the loan is based on a given interest rate, how much you pay per period, and the amount you pay per period.
An annuity loan is paid back for a specific time range at a given interest rate with the same amount for all payments.
The table in cell range E2:H12 shows interest and principal for each period based on values in cell range C2:C4. The total principal (or amortization) paid is the same as the present value in cell C6, which is needed to pay back the entire loan.
Formula in cell C6:
=PV(C3, C4, C5)
The result in cell C6 is the present value of the loan based on the interest rate, periods, and payment amount.
The formula in cell G3 calculates the interest included in each payment.
Formula in cell G3:
=($C$6-SUM($H$2:H2))*$C$2
The principal is what's left after the interest is paid, it is calculated in cell h3.
Formula in cell H3:
=-(F3+G3)
The formulas in cell G15 and H15 adds the amounts and return the total of interest and principal respectively.
Formula in cell G15:
=SUM(G3:G12)
Formula in cell H15:
=SUM(H3:H12)
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6. What anount is needed if I want x in future value, the interest rate is constant, and the number of periods is given?
The image above demonstrates how to use the PV function when you want to know the amount needed for an investment when the interest rate is specified, and the number of periods are given.
Formula in cell C7:
=PV(C2, C3,,C5)
Note that the pmt argument can be empty when you specify the fv (future value) argument in the PV function.
The table, shown in the image above, displays the start amount and the interest for each period. The total accumulates the interest (column F) and the fv (future value) is reached after the given period. The table is not needed for the calculation, it is only there to show that the numbers add up and are correct.
See cell F13, it is equal to the future value in cell C5.
Formula in cell F3:
=-$C$7+SUM($G$2:G2)
Copy cell F3 and paste cells below.
Formula in cell G3:
=$C$2*F3
Copy cell G3 and paste cells below.
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7. What amount is needed if I want x in future value, the interest rate is constant, the payment amount, and the number of periods are given?
The image above shows what amount is needed if you save x amount for each period to reach a future value [fv) given a constant interest rate.
Formula in cell C7:
=PV(C2, C3, C4, C5)
The table in cell range E2:H13 shows that the numbers add up to the future value, specified in cell C5, after the given time of periods based on a constant interest rate.
The table is not needed to calculate the present value of the investment, the PV function is all that is needed.
Formula in cell F3:
=-$C$7+SUM($H$2:H3)+SUM($G$2:G3)
Copy cell F3 and paste to cells below as far as needed.
Formula in cell G4:G13:
=-$C$4
Formula in cell H4:
=$C$2*F3
Copy cell H4 and paste to cells below as far as needed.
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Functions in this article
Functions in 'Financial' category
The PV Function function is one of many functions in the 'Financial' category.
Calculates the accrued interest for a security that pays periodic interest.
Calculates the accrued interest for a security that pays interest at maturity.
Calculates the depreciation for each accounting period. This function is designed for the French accounting system.
Calculates the depreciation for each accounting period.
Calculates the accumulated interest based on a start and end period on a loan.
Calculates the accumulated principal based on a start and end period on a loan.
Calculates the depreciation of an asset for a given period using the fixed-declining balance method.
Calculates the depreciation of an asset for a given period using the double-declining balance method or based on user input.
Converts a decimal number to its equivalent in fractional numbers, used in securities denominated in dollars.
Calculates the effective annual interest rate, given the nominal annual interest rate and the number of compounding periods per year.
Returns the future value of an investment based on a constant interest rate.
Calculates the interest payment for a specific period for an investment based on repeated constant payments and a constant interest rate.
Calculates the interest paid during a specific period of an investment.
Calculates the nominal annual interest rate based on the effective rate and the number of compounding periods per year.
Calculates the number of periods for an investment based on periodic, constant payments and a fixed interest rate.
Calculates how many periods required by an investment to reach a given amount based on a rate in percentage.
Returns the payment needed for borrowing a fixed sum of money based on constant payments (annuity) and interest rate.
Calculates the principal payment for a specific period for an investment based on repeated constant payments and a constant interest rate.
Calculates the price per $100 nominal value of a bond that pays interest at maturity.
Calculates the net present value for an investment or loan.
Returns the interest rate per period of an annuity.
Calculates the growth of an investment in percent per period.
Calculates the yearly asset depreciation of a given year.
Calculates the par amount (face value) for a Treasury bill.
Calculates the yield for a Treasury bill.
Calculates the depreciation of an asset for a given period using the double-declining balance method or based on user input, you may use partial periods in this function.
Calculates net present value for cash flows that may or may not be periodic
Calculates the yield for a security that pays interest. The YIELD function is designed to calculate the bond yield.
Excel function categories
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Functions for backward compatibility with earlier Excel versions. Compatibility functions are replaced with newer functions with improved accuracy. Use the new functions if compatibility isn't required.
Perform basic operations to a database-like structure.
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Let's you manipulate binary numbers, convert values between different numeral systems, and calculate imaginary numbers.
Calculate present value, interest, accumulated interest, principal, accumulated principal, depreciation, payment, price, growth, yield for securities, and other financial calculations.
Functions that let you get information from a cell, formatting, formula, worksheet, workbook, filepath, and other entitites.
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You will find functions in this category that calculates random values, round numerical values, create sequential numbers, trigonometry, and more.
Calculate distributions, binomial distributions, exponential distribution, probabilities, variance, covariance, confidence interval, frequency, geometric mean, standard deviation, average, median, and other statistical metrics.
Functions that let you manipulate text values, substitute strings, find string in value, extract a substring in a string, convert characters to ANSI code among other functions.
Get data from the internet, extract data from an XML string and more.
Excel categories
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Allows you to filter data based on selected value , a given text, or other criteria. It also lets you filter existing data or move filtered values to a new location.
Lets you control what a user can type into a cell. It allows you to specifiy conditions and show a custom message if entered data is not valid.
Lets the user work more efficiently by showing a list that the user can select a value from. This lets you control what is shown in the list and is faster than typing into a cell.
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Lets you quickly summarize vast amounts of data in a very user-friendly way. This powerful Excel feature lets you then analyze, organize and categorize important data efficiently.
VBA stands for Visual Basic for Applications and is a computer programming language developed by Microsoft, it allows you to automate time-consuming tasks and create custom functions.
A program or subroutine built in VBA that anyone can create. Use the macro-recorder to quickly create your own VBA macros.
UDF stands for User Defined Functions and is custom built functions anyone can create.
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