### PV()

*Present value of a loan*

**Syntax**

PV( nPayment, nInterest, nPeriods ) --> nPresentValue

**Arguments**

<nPayment> amount of money paid back per period <nInterest> rate of interest per period, 1 == 100%

<nPeriods> period count

**Returns**

<nPresentValue> Present value of a loan when one is paying back <nDeposit> per period at a rate of interest of <nInterest> per period

**Description**

PV() calculates the present value of a loan that is paid back in <nPeriods> payments of <nPayment> (Dollars, Euros, Yens, …)

while the rate of interest is <nInterest> per period:

debt in period 0 = <nPresentValue>

debt in period 1 = ((debt in period 0)-<nPayment>)*(1+<nInterest>/100)

debt in period 2 = ((debt in period 1)-<nPayment>)*(1+<nInterest>/100) etc…

debt in period <nPeriod> = ((debt in period <nPeriod>-1)-<nPayment>)*(1+<nInterest>/100)

-> has to be 0, so

<nPresentValue> = <nPayment>*(1-(1+<nInterest>/100)ˆ(-n)) / (<nInterest>/100)

**Examples**

// You can afford to pay back 100 Dollars per month for 5 years // at a interest rate of 0.5% per month (6% per year), so instead // of 6000 Dollars (the amount you will pay back) the bank will pay // you ? pv( 100, 0.005, 60 ) // --> 5172.56

**Tests**

pv( 100, 0.0, 60 ) == 6000.0 pv( 100, 0.005, 60 ) == 5172.56

**Compliance**

PV() is compatible with CT3’s PV().

**Platforms**

All

**Files**

Source is finan.c, library is libct.

**Seealso**

FV(), PAYMENT(), PERIODS(), RATE()

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