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Effective Rate of Interest from a Nominal Rate and its Conversion Frequency or the Inverse

eff_rate.Rd

eff_rate() calculates the effective rate of annual interest from a nominal rate and its interest conversion frequency.

nom_rate() calculates the nominal rate of interest for a given interest conversion frequency from an effective rate.

cc_rate() calculates the continuous compounding rate of interest from an effective rate.

Usage

eff_rate(nom_rate, con_fq)

nom_rate(eff_rate, con_fq)

cc_rate(eff_rate)

Arguments

nom_rate

numeric, the nominal interest rate convertible con_fq times per year.

con_fq,

integer, the interest conversion frequency per year.

eff_rate

numeric, the effective rate of interest.

Value

A numeric: eff_rate() returns the effective rate of interest; nom_rate() returns the nominal interest rate convertible con_fq times per year.

Details

Effective Rate of Interest (er): —

$$er = \displaystyle \left(1 + \frac{nr}{ic} \right)^{ic} - 1$$

Nominal Rate of Interest (nr): —

$$nr = \displaystyle \left(\left(1 + er \right)^{\frac{1}{ic}} - 1 \right).ic$$

Continuous Compounding Rate of Interest (ccr): —

$$ccr = \displaystyle e^{er} - 1$$

where \(er\) is the effective rate of interest, \(nr\) is the nominal rate of interest, and \(ic\) is the interest conversion frequency. See amort.period() in package FinancialMath for further details.

References

Investopedia: Effective Annual Interest Rate: Definition, Formula, and Example. www.investopedia.com/terms/e/effectiveinterest

Investopedia: Continuous Compounding Definition and Formula. www.investopedia.com/terms/c/continuouscompounding

See also

amort.period(), amort.table()

Other amort: get_amortval(), j()

Examples

## A lender calculates interest daily using a simple annual rate of 5.7480%,
## based on a 365-day year.

## Calculate effective rate: -
eff_rate(0.057480, 365)
#> [1] 0.05915929

## Calculate nominal rates at monthly and daily interest conversion frequencies: -
## Monthly
nom_rate(0.05915929, 12)
#> [1] 0.05761333
## Daily—same as the original simple annual rate
nom_rate(0.05915929, 365)
#> [1] 0.05748

## Example from https://www.investopedia.com/terms/e/effectiveinterest.asp
eff_rate(0.10, c(2, 4, 12, 365)) |>
    setNames(c("Semiannual", "Quarterly", "Monthly", "Daily"))
#> Semiannual  Quarterly    Monthly      Daily 
#>  0.1025000  0.1038129  0.1047131  0.1051558 

## Limit of compounding (ibid.)
eff_rate(0.1, c(365, 365 * 24, 365 * 24 * 60, 365 * 24 * 60 * 60)) |>
    setNames(c("Daily", "Hourly", "Minutely", "Secondly"))
#>     Daily    Hourly  Minutely  Secondly 
#> 0.1051558 0.1051703 0.1051709 0.1051709 
## Continuous compounding
cc_rate(0.1)
#> [1] 0.1051709