Description Usage Arguments Details Value Author(s)

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.

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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
)
``` |

`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 |

`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 |

`period.no` |
Used only in |

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.

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 |

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

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