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Click to edit Master subtitle style 6/18/11 ACTSC 231 Final Review
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6/18/11 Introduction Jeffrey Baer 3B Actuarial Science Work terms at Manulife and Towers Watson Waterloo SOS President, May 2009 – Aug 2010 5th review session of the term
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6/18/11 Outline 1. Growth of money 2. Equations of value and fund performance 2. Annuities 4. Loan amortization and sinking funds 5. Bonds 6. Spot/forward rates 7. Duration/price sensitivity/immunization
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6/18/11 Growth of Money § Accumulation Functions: § a(0) = 1 and a(t) ≥ a(0) for all t ≥ 0 § Future Value (FV/AV at time t) = a(t) * Present Value (PV) § AK(t) is the FV at time t of $K investment made at time 0 = K * a(t) § a(t) means that our accumulation starts at time 0! § Only works for money invested at (or discounted to) t0
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6/18/11 Compound interest a(t) = (1 + i)t , t ≥ 0 Pays interest on balance earned so far a(t)*a(s) = a(t + s) Example : Edward invests $100 for 2n years at 8% compound interest per year, and
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6/18/11 Effective Rate of Interest The amount of interest payable over a period as a proportion of the balance at the beginning of the period i[n-1, n] = in = Compound: i
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6/18/11 Lian deposits $4,300 into an account on March 1, 1998. The bank guarantees that the annual effective rate for a balance under $5,000 is 3.5% and for a balance over $5,000 is 5%. Suppose that there are no other Effective Rate of Interest
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6/18/11 Discount Rate § Effective rate of discount: d = § Compound discount: a(t) = (1 – d)-t § (1+i)t = (1-d)-t § d= i/(1 + i) i = d/(1 – d)
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6/18/11 Present Value § Discount Functions: § v(t) = 1/a(t) § PV = FV * v(t) § Compound: v(t) = (1+i)-t = § v = v(1) = 1/(1 + i) = 1 – d We can use either discount functions or
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6/18/11 Nominal Rates § Not effective interest rates § Cannot be used directly for PV/AV calculations! § Convertible/compounded mthly: must divide the nominal rate by m to get an effective mthly rate: § (1 + i) = (1 + i(m)/m)m § (1 – d) = (1 – d(m)/m)m
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Force of Interest § Force of Interest § δt = or § a(t) = e ; v(t) = e- § Used for continuous compounding § Compound interest: δ = ln(1+i) => constant § a(t) = eδt ; v(t) = e-δt Example: If the monthly nominal discount rate d(12) is 5%, calculate δ, d(4) and i(1/2). ds S t 0 δ
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6/18/11 Interest Rates Example The accumulated value of $1 at time t (0<=t<=1) is given by a second degree polynomial in t. You are given that the nominal rate of interest convertible semi-annually for the first half of the year is 5% per annum, and the effective rate of interest for the year is 4% per annum.
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6/18/11 Inflation Measures purchasing power of currency Rate of inflation r[t1,t2] = , where Q(t) = value of index (i.e. CPI) at time t Real rate of return j = Effects of inflation have been removed
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6/18/11 Equations of Value PV of cash inflow = PV of cash outflow Example : A single payment of $800 is made to replace 3 payments: $100 in 2 years, $200 in 3 years, and $500 in 8 years.
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This note was uploaded on 06/18/2011 for the course ACTSCI 231 taught by Professor Weng during the Spring '11 term at Whittier.

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Final_Slides - Click to edit Master subtitle style ACTSC...

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