Annuities Due putting it all together.ppt

1、1,Chapter 13 Annuities Due,13.3 putting it all together,2,Annuity classification flowchart P508figure 13.3,3,Example: calculate the time required to pay off a $25,000 loan at 8.25% compounded monthly if the loan is required by A, quarterly payments of $600; B, monthly payments of $200; C,semimonthly

2、 payments of $100; D, in every case, a total of $600 is paid every three months. Explain why the time required to repay the loan shortens as smaller payments are made more frequently.,4,Solution:,A,j=8.25% compounded monthly i=0.6875% per month,FV,PV,n,1/y,PMT,i2,0,25,000,600,97.53,+/-,CPT,n=98 quar

3、ters=24 years and 6 months,5,B,j=8.25% compounded monthly i=0.6875% per month,FV,PV,n,1/y,PMT,0.6875,0,25,000,200,286.31,+/-,CPT,n=287 moths=23 years and 11 months,6,C,j=8.25% compounded monthly i=0.6875% per month,FV,PV,n,1/y,PMT,i2,0,25,000,100,569.58,+/-,CPT,n=570 half months=23 years and 9 month

4、s,7,D,The loans term shortens as a given total annual amount is allocated to smaller, more frequent payments. This happens because the more frequent the payments, the earlier principal balance reduced. Subsequent interest charges are then lower.,8,Example,Victor and his financial adviser are investi

5、gating Victors 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 h

6、is RRSP to purchase a 20-year annuity paying at least $7000 at each months end.,9,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 incom

7、e if the RRSP earns 8% compounded semiannually and the funds used to purchase the annuities earn 7.5% compounded monthly?,10,30,70,60,45,90,age,Annuity 1,Annuity 2,Annuity 3,Annuity 4,FV(due)1,An1,Sn1,An,Sn,Sn1 -An1,(1),(2),(3),(5),(4),Annuities purchased earns 7.5% compounded monthly,RRSP earns 8%

8、compounded semiannually,j=8% compounded semiannually,buy,buy,contribute,contribute,11,Annuity 1: Victor contribute $5000 to his RRSP at the beginning of each year from 30 to 45 years old (general annuity due),Annuity 2: Victor contribute $10,000 at the beginning of each year from 45 to 60 years old

9、(general annuity due),Annuity 3: he will buy a 10-years annuity paying $5000 at the end of each month (ordinary simple annuity),Annuity 4: he will buy a 20-year annuity paying at least $7000 at each months end when he is 70 years old. (ordinary simple annuity),12,Step 1: calculate the future value o

10、f 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,FV,PV,n,1/y,PMT,8.16,15,0,5000,148,680.07,BGN,+/-,FV(due)1=$148,680.07,CPT,13,Step 2: calculate the combined future value of FV(due)1 and annuity 2 when Victor

11、 is 60 years old-Sn1,term=15 years n=15 R=$10,000,FV,PV,PMT,10,000,779,588.71,BGN,+/-,+/-,Sn1 =$779, 588.71,CPT,14,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 yea

12、rs n=120 R=$5000,FV,PV,n,1/Y,PMT,0.625,120,0,5000,-421,223.71,An1 =$421,223.71,CPT,15,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,FV,PV,PMT,358

13、,365,785,221.84,+/-,0,n,1/Y,20,4,Sn =$785,221.84,CPT,16,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,FV,PV,PMT,7000,-868,924.92,0,n,1/Y,240,0.625,An =$868,924.92,CPT,17,Step 6: compare Sn and An when Victor is 70 years old,An =$868,924.92 Sn =$785