calculating-the-number-of-payments.ppt

,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,Chapter 11:Ordinary Annuities:Payment Size,Term,and Interest Rate,11.2 calculating the number of payments,1,Sometimes we need calculate the number of payments of an annuity.,Determining the time required for periodic payments to pay off a loan.,Determining the time required for a periodic savings plan to reach a savings goal.,Determining how long an annuity purchased with a lump investment will deliver a specified payment.,2,Calculating the number of payments,Ordinary annuities,Algebraic method,3,Step 1:calculate the periodic interest rate per payment,step 2:,FV,PV,n,1/y,PMT,results,FV,PV,n,1/y,PMT,R,p,p,R,0,0,FV,PV,Final lump,payment,Initial,lump,payment,Financial calculator method,results,CPT,CPT,4,Example,Roy and Lynn are discussing the terms of a$20,000 home improvement loan with their banks lending officer.The interest rate on the loan will be 12%compounded monthly.,a,how long will it take to repay the loan if the monthly payments are$220?,b,how long will it take to repay the loan if Roy and Lynn pay an extra$20 per month?,5,c,calculate the approximate total of the(nominal)interest savings over the life of the loan as a result of making payments of$240 instead of$220 per month.,6,R=$220 A,n,=$20,000,j=12%compounded monthly,i=p=j/m=1%per month,Solution:,FV,PV,n,i,PMT,240.99,220,1,0,20,000,+/-,It will take 241,payments,requiring,20 years and 1 month,to pay off the loan.,The last payment will,be slightly less than,$220.,Question a:,7,Example,a,Annual contributions of$5000 will be made at every year-end to an RRSP.To the nearest year,how long will it take for the funds in the RRSP to grow to$500,000 if they earn7.5%compounded annually?,10,b,If the$500,000 will be used purchase an annuity earning 8%compounded quarterly and paying$12,000 at the end of each quarter,how long after the purchase date will the annuity payments continue?,11,R=$5000 j=7.5%compounded annually,payment interval=1 year,p=i=j/m=7.5%per year S,n,=$500,000,Solution:,Question a:,FV,PV,n,1/y,PMT,7.5,5000,0,500,000,29.59,+/-,n=30,CPT,12,j=8%compounded quarterly A,n,=$500,000,payment interval=1 quarter R=$12,000,p=i=j/m=2%,Question b:,FV,PV,n,1/Y,PMT,90.48,12,000,2,0,500,000,+/-,91/4=22.75 years,=22 years,9 months,CPT,13,Example,If,1 month from now,Maurice makes the first monthly contribution of$250 to an RRSP that earns 8%compounded annually,how long will it take him to accumulate$100,000?,14,j=8%compounded annually R=$250,i=j/m=8%per year S,n,=$100,000,payment interval=1 month,Solution:,15,Financial calculator method,FV,+/-,n,1/Y,PMT,250,0.6434,0,100,000,PV,198.58,It will take 199 months to accumulate,$100,000.And the last contribution,will be less than$250.,CPT,16,Example,$10,000 is invested in a fund earning,9.25%,compounded semiannually,.Five years later the first,semiannual withdrawal,of$1000 is taken from the fund.After how many withdrawals will the fund be depleted?(The final payment that extinguishes the fund will be smaller than$1000.Include it in the count.),17,Solution:,0,5.5,4.5,5,year,$1000,$1000,A,n,j=9.25%compounded,semiannually,p=i=j/m=4.125%,term of the deferral,=4.5 years,d=9 R=$1000,A,n,(def)=$10,000,18,Financial calculator method,Step 1:calculate A,n,.,Step 2:calculate n,PV,PMT,n,10,000,9,15,021.71,FV,0,1/Y,4.125,p=4.125%d=9,A,n,(due)=$10,000,+/-,p=4.125%,A,n,=$15,021.71,R=$1000,PV,PMT,n,+/-,0,FV,1000,26.25,n=27,CPT,CPT,19,The fund will be depleted after 27 withdrawals.,The last withdrawal will be smaller.It is,$1000*.025=$250.,20,