# PV()

### 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()