# Actuary Exam #2 Formulas

## 37 terms

PV(1 + i)ⁿ

FV / (1 + i)ⁿ

### a(t) continuous basis:

(1+i)^t = e^(tln(1+i) = e^(δt)

(1+it)

### Effective rate for time period:

(a(t+1) - a(t)) / a(t)

### Convert Nominal rate to Effective Rate i=

(1+ (i^m/m))^m -1

i/(1+i)

1/(1+i)

### 3 Relationships of v,d,i:

d + v = 1, d = iv, i-d = id

### Effective discount rate:

1 - d = (1 - (d^m/m))^m

### Convert nominal to discount:

(1 + (i^m/m))^m = (1- (d^p/p))^-p

ln(1+i)

a'(t) / a(t)

### Given δ(t), a(t) =

e^ integral(δ(u) du) from 0 - t

e^)nδ)

### continuous: v^n =

(1+i)^-n = e^(-nδ)

(e^i - 1)

### Relationship of d & I's

d < d^m < δ < i^m < i

### Geometric Series 1 + r + r^2 + ......+ =

(1 - r^(n+1))/(1-r).........if [r] < 1: = 1/(1-r)

### an¬=

(1 - v^n)/i = v^n(sn¬)

### sn¬=

(1+i)^n (an¬) = ((1+i)^n - 1)/i

1/i

### ä∞¬=

i/d(a∞¬) = (1+i)(a∞¬)

### än¬=

(1-v^n)/d = (i/d)(an¬)

### s:n¬=

(1+i)^n (än¬) = ((1+i)^n - 1)/d = (i/d)(sn¬)

### ān¬=

(1-v^n)/δ = (i/δ)(an¬)

### ŝn¬=

((1+i)^n -1)/δ = (i/δ)(sn¬)

1/δ = (i/δ)a∞¬

(än¬ - nv^n)/i

### (Is)n¬=

(1+i)^n(Ia)n¬ = (s:n¬ - n)/i

### (Iä)n¬=

i/d(Ia)n¬ = (1+i)(Ia)n¬ = (än¬ - nv^n)/d

### (Is:)n¬=

(1+i)^n(Iä)n¬ = (s:n¬ - n)/d = (i/d)(Is)n¬

(n- an¬)/i

((1+i)^n)(Da)n¬

### (Dä)n¬=

(n- an¬)/d = (1+i)(Da)n¬

((1+i)^n)(Dä)n¬

### Annuity with 1st payment P and subsequent payments Q =

Pan¬ + Q*((an¬-nv^n)/i)