SOA Exam FM Questions & Answers | Financial Mathematics Study Guide

SOA Exam FM Questions & Answers

effective rate of interest (A(t) - A(t-1))/(A(t-1))

effective rate of discount (A(n)-A(n-1))/A(n)

Accumulation and Amount A(t) = A(0)*a(t)
Function

Simple interest a(t) = 1+it

Variable Force of interest 𝛿_t = a'(t)/a(t)

Accumulation of variable force e^(∫_t₁^t₂ δ_u du)
of interest

v 1/(1+i) = 1-d

d i/(1+i) = iv

i real (1+i)/(1+π) -1

real interest rate i = (i + i_real ) ( 1+π)-1

a angle n (1-v^n) / i

s angle n ((1+i)^n - 1 )/i

a double dot angle n (1-v^n)/d

s double dot angle n ((1+i)^n -1)/d

due to immediate a double ( a angle n )(1+i) = 1 + a angle n -1
dot angle n

due to immediate s double dot (s angle n)(1+i) = s angle (n +1) - 1
angle n

a angle infinity 1/i

a double dot angle infinity 1/d

due to immediate a double 1 + a angle infinity
dot angle infinity

PV of payments in arithmetic P a angle n + Q ( a angle n - n v^n )/ i
progression

P and Q method PV P+Q/i

P and Q method FV -Qn / i

Ia angle n (a double dot angle n - nb^n)/ i

Da angle n (n - a angle n) / i

Ia angle infinity 1/ id = P/i + Q/i^2

I double dot a angle infinity 1 / d^2




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