# PAYMENT()

### PAYMENT()

Payments for a loan

Syntax

`       PAYMENT( nLoan, nInterest, nPeriods ) --> nPayment`

Arguments

<nLoan> amount of money you get from the bank

<nInterest> rate of interest per period, 1 == 100%

<nPeriods> period count

Returns

<nPayment> Periodical payment one has to make to pay the loan <nLoan> back

Description

PAYMENT() calculates the payment one has to make periodically to pay back a loan <nLoan> within <nPeriods> periods and for a rate of interest <nInterest> per period.

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

Examples

```       // You get a loan of 5172.56 at a interest rate of 0.5% per
// month (6% per year).
// For 5 years, you have to pay back every month

? payment( 5172.56, 0.005, 60 ) // --> 100.00```

Tests

```       payment( 5172.56, 0.0, 60 )   == 86.21
payment( 5172.56, 0.005, 60 ) == 100.00```

Compliance

PAYMENT() is compatible with CT3’s PAYMENT().

Platforms

All

Files

Source is finan.c, library is libct.

Seealso

PV(), FV(), PERIODS(), RATE()