MATH419: Actuarial Science. Exam-FM Formulas

math419 : Actuarial FormulasInterest:sum of geometric seriesSn=a(1 rn)/(1 r) Compound:A(t) =A(0)(1 +i)t=A(0)(1 d) tSimple:A(t) =A(0)(1 +it) v=11+idiscountd= 1 force of interest = ln(1 +i). varying force of interest (t) =dA/dtA(t).separate and integrateA(t) =A(0)e t0 (s)ds. interest earned fromatob=A(b) A(a).Xdeposited ataaccumulated tillbisA(b) =Xe ba (s)dsLevel Annuities:5-button formulaPV=PMTan+Fvn PV immediatean=1 vniPV due an= (1 +i)ancontinuously paidan=an(i ) FVsn= (1 +i)nan=(1+i)n 1i sn=(1+i)n 1dperpetuitya =1i a =1d a(m)nmeansmpayments per year (12)nominal meansi(12)12interest per monthVarying Annuities:CF button, to enter PMTs and frequency.

Ch4: Hedging reasons to hedge: risk-aversion, distress costs, costly external nancing, increase debt capacity, tax. reasons NOT to hedge: transaction costs, bid/ask ...

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