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syntax:functions:pv

# PV(rate, num_per, payment)

Category: Number (Financial) function

## Description

This function calculates the present value of a loan or an investment, based on a constant interest rate.

Optional future value (fut_val) argument.

`pv(rate, num_per, payment, fut_val)`

Optional payments due (pay_due) argument.

`pv(rate, num_per, payment, fut_val, pay_due)`

## Arguments

ArgumentTypeDescription
rateNumber (decimal)The interest rate of the loan (entered as a decimal).
num_perNumberThe number of payments of the loan (usually in months or years).
paymentNumber (negative)The payment made each period (that does not change), entered as a negative value. Includes principal
and interest, but no fees or taxes.
fut_valNumberOptional. The future value, or cash balance, to be achieved after the last payment (i.e., "0" to pay the loan
off in full). The default, if not supplied, is 0.
pay_dueBinary (0 or 1)Optional. This value defines when payments are due. Options: 0 (the beginning of the period; default),
or 1 (the end of the period).

Return value type: Number

## Remarks

For an accurate calculation, be sure to convert rate and num_per to the same time period. If calculating a monthly payment and rate is an annual rate, divide it by 12 (rate / 12). If num_per is given as years, multiply by 12 (num_per * 12).

## Examples

Calculate the present value: Interest rate is 10% (annual), number of periods is 36 (months), payment is \$225 per month.

`pv( (0.10/12), 36, -225) //Returns \$6973.03 (months, rounded)`

Calculate the present value: Interest rate is 14% (annual), payment is \$6000 per year, final value is \$30,000.

`pv(0.14, 10, -6000, 30000) //Returns \$23,204.38 (rounded)`

Calculate the present value: Interest rate is 1% (monthly), payment \$600 per month, final value is \$21,000, payments due at the end of the period.

`pv(0.01, 48, -600, 21000, 1) //Returns \$9986.75 (rounded)` 