interest

Interest Theory - Applies interest rate formulas

class actuarialmath.interest.Interest(i: float = -1.0, delta: float = -1.0, d: float = -1.0, v: float = -1.0, i_m: float = -1.0, d_m: float = -1.0, m: int = 0, v_t: Callable[[float], float] | None = None)[source]

Bases: Actuarial

Store an assumed interest rate, and compute interest rate functions

Parameters:

i – assumed annual interest rate
d – or annual discount rate
v – or annual discount factor
delta – or continuously compounded interest rate
v_t – or discount rate as a function of time
i_m – or m-thly interest rate
d_m – or m-thly discount rate
m – m’thly frequency, if i_m or d_m are specified

property i: float: effective annual interest rate

property d: float: annual discount rate of interest

property delta: float: continuously compounded interest rate, or force of interest, per year

property v: float: annual discount factor

property v_t: Callable: discount factor as a function of time

annuity(t: int = -1, m: int = 1, due: bool = True) → float[source]

Compute value of the annuity certain factor

Parameters:

t – number of years of payments
m – m’thly frequency of payments (0 for continuous payments)
due – whether annuity due (True) or immediate (False)

Examples

>>> print(interest.annuity(t=10, due=False), 2.831059)

static mthly(m: int = 0, i: float = -1, d: float = -1, i_m: float = -1, d_m: float = -1) → float[source]

Convert to or from m’thly interest rates

Parameters:

m – m’thly frequency
i – an annual-pay interest rate, to convert to m’thly
d – or annual-pay discount rate, to convert to m’thly
i_m – or m’thly interest rate, to convert to annual pay
d_m – or m’thly discount rate, to convert to annual pay

Examples

>>> i = Interest.mthly(i_m=0.05, m=12)
>>> print("Convert mthly to annual-pay:", i)
>>> print("Convert annual-pay to mthly:", Interest.mthly(i=i, m=12))

static double_force(i: float = -1.0, delta: float = -1.0, d: float = -1.0, v: float = -1.0)[source]

Double the force of interest

Parameters:

i – interest rate to double force of interest
d – or discount rate
v – or discount factor
delta – or continuous rate

Returns:

interest rate, of same form as input rate, after doubling force of interest

Examples

>>> print("Double force of interest of i =", Interest.double_force(i=0.05))
>>> print("Double force of interest of d =", Interest.double_force(d=0.05))