notes on annuities

# notes on annuities - 0 1 2 3 4 5 \$1 \$1 \$1 \$1 \$1 \$1 Present...

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Present Value: Ordinary annuity: Suppose you have an annuity that pays \$1 in the end of every year for 6 years. The interest rate is 10%. What is the present value of that annuity? 0 6 \$1 \$1 \$1 \$1 \$1 \$1 Present value of \$1 paid in the end of year 1: 91 . 0 \$ ) 1 . 0 1 ( 1 \$ 1 = + Present value of \$1 paid in the end of year 2: 83 . 0 \$ ) 1 . 0 1 ( 1 \$ 2 = + Present value of \$1 paid in the end of year 3: 75 . 0 \$ ) 1 . 0 1 ( 1 \$ 3 = + Present value of \$1 paid in the end of year 4: 68 . 0 \$ ) 1 . 0 1 ( 1 \$ 4 = + Present value of \$1 paid in the end of year 5: 62 . 0 \$ ) 1 . 0 1 ( 1 \$ 5 = + Present value of \$1 paid in the end of year 6: 56 . 0 \$ ) 1 . 0 1 ( 1 \$ 6 = + The total value of an annuity thus is \$0.91+\$0.83+\$0.75+\$0.68+\$0.62+\$0.56=\$4.36 Compare it to the undiscounted value of \$6 (one dollar each period). The difference of \$6-\$4.36=\$1.64 is the cost of time value of money.

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Annuity due Suppose you have an annuity that pays \$1 in the beginning of every year for 6 years. The interest rate is 10%. What is the present value of that annuity?
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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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notes on annuities - 0 1 2 3 4 5 \$1 \$1 \$1 \$1 \$1 \$1 Present...

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