Annuity Due vs. Ordinary Annuity Ordinary Annuity is standard for most set- ups and implies payment at the end of the period Annuity Due is payment at the beginning of the period Both have the following characteristics Regular Interval Regular Interval Same Amount Same Amount

Annuity Due vs. Ordinary Annuity Look at time line for the cash flows… Note the difference between the two streams Note the difference between the two streams Same number of total payments Same number of total payments Annuity Due has a payment at T 0 Annuity Due has a payment at T 0 Ordinary Due has a payment at T N Ordinary Due has a payment at T N All other Payments are the same! All other Payments are the same! Adjusting the FVIFAs and PVIFAs Note the tables and formulas are for Ordinary Annuity Streams Note the tables and formulas are for Ordinary Annuity Streams

Annuity Due vs. Ordinary Annuity FVIFA adjustment The entire annuity stream receives one additional time period of interest earnings: The entire annuity stream receives one additional time period of interest earnings: Take Ordinary Annuity FVIFA x (1 +r) Take Ordinary Annuity FVIFA x (1 +r) Or ((1+r) N – 1 ) / r) x (1+ r) Or ((1+r) N – 1 ) / r) x (1+ r) For the calculator just set Mode to BGN For the calculator just set Mode to BGN Second Function above PMT Then second and enter Example…$100 for ten years at 10%. Example…$100 for ten years at 10%.

Annuity Due vs. Ordinary Annuity PVIFA Adjustment The entire annuity stream receives one less discount over the time period or you have an ordinary annuity of n-1 and a lump sum at T 0 The entire annuity stream receives one less discount over the time period or you have an ordinary annuity of n-1 and a lump sum at T 0 Take Ordinary Annuity PVIFA for n-1 and add PMT for T 0 Take Ordinary Annuity PVIFA for n-1 and add PMT for T 0 Or PMT (1- /1(1+r) N-1 – 1 ) / r) + PMT Or PMT (1- /1(1+r) N-1 – 1 ) / r) + PMT Or PVIFA = (1- /1(1+r) N-1 – 1 ) / r) + 1 Or PVIFA = (1- /1(1+r) N-1 – 1 ) / r) + 1 Example…$100 for ten years at 10%. Example…$100 for ten years at 10%.

Interest Rates Term Structure of Interest Rates (Yield Curve) Rates vary with time Rates vary with time Typically long-term rates higher than short-term rates Typically long-term rates higher than short-term rates Problem 6.1 – Draw Yield Curve Problem 6.1 – Draw Yield Curve Theories of Term Structure Expectations Hypothesis Expectations Hypothesis Liquidity Preference Liquidity Preference Market Segmentation Market Segmentation Different instruments different rates Risk of Cash Flows Risk of Cash Flows Higher Risk investor demands Higher Return Higher Risk investor demands Higher Return

Interest Rates Annual Percentage Rate Effective Annual Rate Nominal Interest Rate Real Interest Rate Risk-Free Interest Rate Risk Premium (s) Inflation Rate Fisher Effect: 1 + nominal = (1 + real) x (1 + inf.)