常用公式大全form1(SOA北美精算师考试handbook notes)

STA4183–The Theory of Interest

Basic Formulas

Accumulation function a(t),a(0)=1Simple interest a(t)=1+it Amount function A(t)=A(0)·a(t)Simple discount d(t)=1−dt

Effective rate i n=a(n)−a(n−1)

a(n−1)

Compound interest a(t)=(1+i)t

of interest

i=i11+i=

1+

i(m)

m

m

Discount function d(t)=

1

a(t)

Compound discount d(t)=(1−d)t

Effective rate d n=a(n)−a(n−1)

a(n)

1−d=

1−

d(m)

m

m

of discount

d=d1Force of Interestδ(t)=a (t) a(t)

d=

i

1+i

,i=

d

1−d

a(t)=e

t

δ(s)ds