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**Unformatted text preview: **0 1 2 3 4 5 $1 $1 $1 $1 $1 $1 Present value of $1 paid in the beginning of year 1: $1 Present value of $1 paid in the beginning of year 2: 91 . $ ) 1 . 1 ( 1 $ 1 = + Present value of $1 paid in the beginning of year 3: 83 . $ ) 1 . 1 ( 1 $ 2 = + Present value of $1 paid in the beginning of year 4: 75 . $ ) 1 . 1 ( 1 $ 3 = + Present value of $1 paid in the beginning of year 5: 68 . $ ) 1 . 1 ( 1 $ 4 = + Present value of $1 paid in the beginning of year 6: 62 . $ ) 1 . 1 ( 1 $ 5 = + The total value of an annuity thus is $1+ $0.91+$0.83+$0.75+$0.68+$0.62=$4.79 Compare it to the undiscounted value of $6 (one dollar each period). The difference of $6-$4.79=$1.21 is the cost of time value of money. Note also that annuity due is more valuable since payments occur earlier than in ordinary annuity...

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