Annuities Due putting it all together参考.ppt

Chapter 13 Annuities Due 13.3 putting it all together Example Victor and his financial adviser are investigating Victor’s ability to achieve his goals for retirement income. He wishes to retire in 30 years at age 60. His plan is to use some of the funds in his RRSP at that time to purchase a 10-year annuity paying $5000 at the end of each month. Then, at age 70, he would use the balance of the funds in his RRSP to purchase a 20-year annuity paying at least $7000 at each month’s end. Victor anticipates that he can contribute $5000 to his RRSP at the beginning of each of the next 15 years and $10,000 at the beginning of each of the subsequent 15 years. Can Victor achieve the desired retirement income if the RRSP earns 8% compounded semiannually and the funds used to purchase the annuities earn 7.5% compounded monthly? Step 1: calculate the future value of annuity 1 FV(due)1 j=8% compounded semiannually i=j/m=4% per half year payment interval=1 year term=15 years p=(1+i)c-1=8.16% n=15 R=$5000 Step 2: calculate the combined future value of FV(due)1 and annuity 2 when Victor is 60 years old--Sn1 term=15 years n=15 R=$10,000 Step 3: calculate the present value of annuity 3 when Victor is 60 years old--An1 j=7.5% compounded monthly i=j/m=7.5%/12=0.625% per month payment interval=1 month p= 0.625 % term=10 years n=120 R=$5000 Step 4: calculate the future value of Sn1 - An1 when he is 70 years old-- Sn PV= Sn1 -An1 =$358,365 the remaining funds earns 8% compounded semiannually i=j/m=4% per compounding term=10 years n=10*2=20 Step 5: calculate the present value of annuity 4 when Victor is 70 years old--An j=7.5% compounded monthly i=j/m=7.5%/12=0.625% per month payment interval=1 month p= 0.625 % term=20 years n=240 R=$7000 Step 6: compare Sn and An when Victor is 70 years old An =$868,924.92 Sn =$785,221.84 An Sn When Victor is 70 years old, the remaining funds in his RRSP is $785,2