Simplifications(2) Annuity -a level stream of regular payments lasting for a fixed number of periods vc Growing Annuity pv-clg 1+g 1+r slide 15
slide 15 Simplifications (2) Simplifications (2) Annuity -- a level stream of regular payments lasting for a fixed number of periods Growing Annuity ] )1(* 11[* t rrr CPV + −= T r g grgr CPV ) 1 1(* 11 [* + + − − − =
Case Study (1) Harold and Helen are saving for the college education of their newborn daughter,Susan.They estimate that college expenses will run $30,000 per year when their daughter reaches college after 18 years.The annual interest rate over the next few decades will be 14 percent.How much money must they deposit in the bank each year so that their daughter will be supported? slide 16
slide 16 Case Study (1) Case Study (1) Harold and Helen are saving for the college education of their newborn daughter, Susan. They estimate that college expenses will run $30,000 per year when their daughter reaches college after 18 years. The annual interest rate over the next few decades will be 14 percent. How much money must they deposit in the bank each year so that their daughter will be supported?
Case Study (1) 1.To calculate the present value of the four years at college using the annuity formula. PV=$30,000*[ 0.14*(1+0.14) 4]=$87,411 0.14 2.To calculate the PV at date 0 as $87,411 PV= $9,422.91 (1+0.14)7 slide 17
slide 17 Case Study (1) Case Study (1) 1. To calculate the present value of the four years at college using the annuity formula. 2. To calculate the PV at date 0 as 411,87$] )14.01(*14.0 1 14.0 1 [*000,30$ 4 = + PV = − 91.422,9$ )14.01( 411,87$ 17 = + PV =
Case Study (1) 3.To calculate the annual deposit at the end of each of the 17 years C=$9,422.91/[ 7]=$1,478.59 0.14 0.14*(1+0.14) 4.If they plan to increase their payments at 4%per year. 1.04 $9,422.91=C*[ .14-0.04 0.14-0.04 1.14 C=$1,192.78 slide 18
slide 18 Case Study (1) Case Study (1) 3. To calculate the annual deposit at the end of each of the 17 years 4. If they plan to increase their payments at 4% per year. 59.478,1$] )14.01(*14.0 1 14.0 1 /[91.422,9$ 17 = + C = − 78.192,1$ ) 14.1 04.1(* 04.014.0 1 04.014.0 1 [*91.422,9$ 17 = − − − = C C
ls it correct (1) 1.To calculate the present value of the four years at college using the annuity formula. PV=$30,000*[ 0.14*(1+0.14) 4]=$87,411 0.14 2.To calculate the PV at date 0 as $87,411 PV= =$10,742.08 (1+0.14)16 slide 19
slide 19 Is it correct (1) Is it correct (1) 1. To calculate the present value of the four years at college using the annuity formula. 2. To calculate the PV at date 0 as 411,87$] )14.01(*14.0 1 14.0 1 [*000,30$ 4 = + PV = − 08.742,10$ )14.01( 411,87$ 16 = + PV =