# annuity: Present Value of Annuity and Related Functions In jrvFinance: Basic Finance; NPV/IRR/Annuities/Bond-Pricing; Black Scholes

## Description

Functions to compute present value and future value of annuities, to find instalment given the present value or future value. Can also find the rate or the number of periods given other parameters.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63``` ```annuity.pv( rate, n.periods = Inf, instalment = 1, terminal.payment = 0, immediate.start = FALSE, cf.freq = 1, comp.freq = 1 ) annuity.fv( rate, n.periods = Inf, instalment = 1, terminal.payment = 0, immediate.start = FALSE, cf.freq = 1, comp.freq = 1 ) annuity.instalment( rate, n.periods = Inf, pv = if (missing(fv)) 1 else 0, fv = 0, terminal.payment = 0, immediate.start = FALSE, cf.freq = 1, comp.freq = 1 ) annuity.periods( rate, instalment = 1, pv = if (missing(fv)) 1 else 0, fv = 0, terminal.payment = 0, immediate.start = FALSE, cf.freq = 1, comp.freq = 1, round2int.digits = 3 ) annuity.rate( n.periods = Inf, instalment = 1, pv = if (missing(fv)) 1 else 0, fv = 0, terminal.payment = 0, immediate.start = FALSE, cf.freq = 1, comp.freq = 1 ) annuity.instalment.breakup( rate, n.periods = Inf, pv = 1, immediate.start = FALSE, cf.freq = 1, comp.freq = 1, period.no = 1 ) ```

## Arguments

 `rate` The interest rate in decimal (0.10 or 10e-2 for 10%) `n.periods` The number of periods in the annuity. `instalment` The instalment (cash flow) per period. `terminal.payment` Any cash flow at the end of the annuity. For example, a bullet repayment at maturity of the unamortized principal. `immediate.start` Logical variable which is `TRUE` for immediate annuities (the first instalment is due immediately) and `FALSE` for deferred annuities (the first instalment is due at the end of the first period). `cf.freq` Frequency of annuity payments: 1 for annual, 2 for semi-annual, 12 for monthly. `comp.freq` Frequency of compounding of interest rates: 1 for annual, 2 for semi-annual, 12 for monthly, Inf for continuous compounding. `pv` The present value of all the cash flows including the terminal payment. `fv` The future value (at the end of the annuity) of all the cash flows including the terminal payment. `round2int.digits` Used only in `annuity.periods`. If the computed number of periods is an integer when rounded to round2int.digits, then the rounded integer value is returned. With the default value of 3, 9.9996 is returned as 10, but 9.9994 and 9.39999999 are returned without any rounding. `period.no` Used only in `annuity.instalment.breakup`. This is the period for which the instalment needs to be broken up into principal and interest parts.

## Details

These functions are based on the Present Value relationship:

pv = fv * df = terminal.payment * df + instalment * (1 - df) / r

where df = (1 + r)^{-n.periods} is the n.periods discount factor and r is the per period interest rate computed using rate, cf.freq and comp.freq.

It is intended that only one of pv or fv is used in any function call, but internally the functions use pv + fv * df as the LHS of the present value relationship under the assumption that only of the two is non zero.

The function `annuity.instalment.breakup` regards the annuity as a repayment of a loan equal to `pv` plus the present value of terminal.payment. The instalment paid in period period.no is broken up into the principal repayment (amortization) and interest components.

## Value

For most functions, the return value is one of the arguments described above. For example `annuity.pv` returns `pv`. The only exception is `annuity.instalment.breakup`. This returns a list with the following components:

 `opening.principal` The principal balance at the beginning of the period `closing.principal` The principal balance at the end of the period `interest.part` The portion of the instalment which represents interest `principal.part` The portion of the instalment which represents principal repayment

## Author(s)

Prof. Jayanth R. Varma jrvarma@iima.ac.in

jrvFinance documentation built on April 18, 2021, 5:06 p.m.