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ACTUARIAL EXAM FM FORMULAS QUESTIONS AND VERIFIED ANSWERS|100% CORRECT|GRADE A+
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ACTUARIAL EXAM FM FORMULAS QUESTIONS AND VERIFIED ANSWERS|100% CORRECT|GRADE A+
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ACTUARIAL EXAM FM FORMULASQUESTIONS AND VERIFIED
ANSWERS|100% CORRECT|GRADE A+
Effective Rate of Interest - ANSWER i_t= [(A(t)-A(t-1)]/A(t-1)
effective rate of interest equals accumulated amount at time t minus the accumulated amount at time t-
1 all over accumulated amount at time t-1
Effective Rate of Discount - ANSWER d_t= [(A(t)-A(t-1)]/A(t)
effective rate of interest equals accumulated amount at time t minus the accumulated amount at time t-
1 all over accumulated amount at time t
Accumulation/Amount Function - ANSWER A(t) = A(0)*a(t)
Accumulated amount equals amount at times the accumulation function
Simple Interest - ANSWER a(t) = 1+i*t
accumulation function equals 1 plus interest * times t
Variable Force of Interest - ANSWER 𝛿_t = a'(t)/a(t)
delta equals a prime over a
Variable Force of Interest Accumulated Over Specified Time Period - ANSWER Accumulating 1 from t_1
to t_2
FV = e^(t_1/int/t_2 𝛿_u du)
, Future Value from time t_1 to t_2 equals e to the integral from t_1 to t_2 of 𝛿_u du
Discount Factors - ANSWER v = 1/(1+i) = 1-d
d = i/(1+i) = iv
PV of Annuity Immediate - ANSWER PV = a∟n
= v^1+v^2+v^3+...+v^n
= (1-v^n)/i
FV of Annuity Immediate - ANSWER FV = s∟n
= 1+(1+i)^1+(1+i)^2+(1+i)^3+...+(1+i)^n-1
= ((1+i)^n-1)/i
PV of Annuity Due - ANSWER PV = a..∟n
= 1+v^1+v^2+v^3+...+v^n-1
= (1-v^n)/d
FV of Annuity Due - ANSWER FV = s..∟n
= (1+i)^1+(1+i)^2+(1+i)^3+...+(1+i)^n-1
= ((1+i)^n-1)/d
Annuities Immediate and Due Relationships - ANSWER a..∟n = a∟n*(1+i) = 1 + a∟(n-1)
s..∟n = s∟n*(1+i) = 1 + s∟(n+1)-1
Deferred Annuity - ANSWER m-year deferred n-year annuity
PV = m_a∟n = v^m*a∟n = a∟(n+m)-a∟m
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