ACTUARIAL EXAM FM FORMULAS QUESTIONS AND VERIFIED ANSWERS|100% CORRECT|GRADE A+

ACTUARIAL EXAM FM FORMULAS
QUESTIONS 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