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.
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
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