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Unformatted text preview: e of Annuities
• Suppose that you want to find the future value of an nyear regular annuity.
– The future value factor for annuity (for n payments), FAF(r,n), is given by FAF( r , n) = (1 + r ) n −1 + (1 + r ) n−2 +...+(1 + r ) + 1 = 1 n × (1 + r ) − 1 r [ 7 Future Value of Annuities • Thus, the future value of an nyear annuity is:
FV = C × FAF(r, n) Example: Sinking Funds Suppose that you want to guarantee yourself $500,000 when you retire 40 years from now. How much must you invest each year, starting at the end of this year, if the interest rate is 6%? Present Value of Annuities • Present Value Calculation
Year
1 2 3 Cash Flow Years to Discount: n
C C C 1 2 3 Present Value
C 1+ r
C (1 + r) 2 C (1 + r) 3 8 Present Value of Annuities • Applying the addition principle, we have that the present value of this three years regular annuity is
PV = C C C + + 1 + r (1 + r ) 2 (1 + r ) 3 ⎡1 1 1⎤ = C×⎢ + + ⎥ 1 + r (1 + r ) 2 (1 + r ) 3 ⎦ ⎣ Present Value of Annuities
– The present value factor for annuity (for n periods), PAF(r,n), is
PAF( r , n) = 1 1 1 + +...+ 1 + r (1 + r ) 2 (1 + r ) n 1⎡ 1⎤ = × ⎢1 − ⎥ r ⎣ (1 + r ) n ⎦ Present Value of Annuities • Therefore, the present value of an nyear annuity is
PV = C × PAF( r , n) 9 Example: Capital Recovery • You plan to attend a pricey graduate school of business and you will be for...
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This note was uploaded on 01/17/2011 for the course MGMT 107 taught by Professor ? during the Winter '08 term at UC Irvine.
 Winter '08
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