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Chapter 13 Annuities Due 13.2 present value of an annuity due Present value of an annuity due Present Value Using the Algebraic Method Present value of an annuity due Present value using the financial calculator functions Application of the present-value calculation The market value of an annuity The economic value of an annuity Example A lottery offers the winner a choice between a $300,000 cash prize or quarterly payments of $7000 beginning immediately and continuing for 20 years. Which alternative should the winner pick if money is worth 8% compounded annually? Example Mayfair Furniture is advertising a chesterfield and reclining chair combination for $131.83 down and 11 monthly payments of $131.83, including interest at 15% compounded annually. What is the ticket or cash price of the set? Solution: Example An annuity will pay $1000 at the end of June 2003 and every 6 months thereafter up to and including a payment at the end of June 2016. To the nearest dollar, what will be the economic value of the annuity on June 30,2003, if money will be worth 8% compounded quarterly for the first 5 years and 8% compounded semiannually for the remainder of the annuity’s term? Solution: Step 1: calculate the present value of all payments are made during the first 5 years j=8% compounded quarterly i=8%/4=2% p=(1+i)c-1=4.04% R=$1000 n=5*2=10 Step 2:calculate the present value of all payments made during the subsequent 8 years on June, 30, 2008 n=(2015-2008+1)*2+1=17 R=$1000 j=8% compounded semiannually i=p=8%/2=4% Step 3: discount PV2(due) on June 30,2003 at 8% compounded quarterly n=5*4=20 j=8% compounded quarterly i=j/m=8%/4=2% Step 4: the economic value of all payments on June 30, 2003 is the sum of PV and An1(due) PV+ PV1(due) =$8514.63+$8421.80=$16,936.43 The book value of a lease At any point during the term of the lease, the present value of the remaining lease payments