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1、Chapter 11 Ordinary Annuities: Payment Size, Term, and Interest Rate11.1 calculating the periodic payment1Some circumstances in which the periodic payment, R, must be calculate are:Determiningthe monthly payments on a loanDetermining the amount that must be saved on a regular basis to reach a saving
2、 goalDetermining the periodic payment from an annuity purchased with a lump investment.2calculating the periodic paymentAlgebraic methodStep 1: calculate the periodic interest rate per payment intervalStep 2: substitute known valuesintoStep 3: rearrange the equation tosolve for R.3Step 1: calculate
3、the periodic interest rate per payment-Pstep 2: FVPVn1/yPMTFVPVn1/yPMTnppn00FVFinancial calculator methodFinal lump paymentInitial lump paymentresultsresultsPVCPTCPT4Example Markham Auto Body wishes to accumulate a fund of $150,000 during the next 18 months in order to open at a second location. Wha
4、t constant amount should it pay at the end of each month into a money market savings account with an investment dealer, in order to attain its savings objective? The planning assumption is that the account willearn 4.8% compounded monthly.5Sn=$150,000 j=4.8% compounded monthlyi=j/m=4.8%/12=0.4%=p n=
5、18 Solution:Algebraic methodFinancial calculator methodFVPVn1/YPMT0.4180150,000-8053.58CPT6ExampleMr. and Mrs. Moris obtain a $20,000 home improvement loan from their bank at an interest rate of 7.5% compounded monthly.What amount paid monthly will reduce the balance to $10,000 after 5 years?7012345
6、year$10,000 Monthly paymentsAnPVAn+ PV=$20,000Solution:8Algebraic method:Step 1: calculate AnStep 2: calculate PVPV=present value of $10,000P=i=j/m=0.625%9Step 3:R=$262.88Payments of $262.88 will reduce the balance to $10,000 after 5 years.An+ PV=$20,00010Financial calculator methodFVniPMT600.625510
7、,00020,000-262.88+/-PVCPT11ExampleDouglas and Margaret have already accumulated $125,000 in their RRSP. They are attempting to estimate the annual contributions they must make in order to retire in 15 years, when Doug turns 60. Their goal is to have enough funds in the RRSP to purchase a 25-year ann
8、uity that will pay $5000 at the end of each month. The planning assumptions12are an 8% annually compounded return on their RRSP and an 8.1% monthly compounded return on the annuity purchased with their RRSP funds. What combined RRSP contributions should they make at the end of each of the next 15 ye
9、ars?13Solution:01231540year$125,000RRRR $5000 $5000$5000SnAnSAnnuity 2Annuity 1j=8.0% compounded annuallyj=8.1% compounded monthly12300monthSn+S=An 14Step 1: calculate the future value of annuity 1-SnTerm=15 years n=15 j=8.0% compounded annually i=j/m=8.0%15Step 2: calculate the future value of $125
10、,000 at the focal date -STerm=15 years n=15 j=8.0% compounded annually i=j/m=8% PV=$125,00016Step 3: calculate the present value of annuity 2 at the focal date-AnTerm=25 years n=25*12=300payment interval=1 monthR=$5000 j=8.1% compounded monthly p=i=j/m=8.1%/12=0.675% per month17Step 4: substitute th
11、ese values for An, S, Sn into Sn+S=AnThe annual contributions is $9051.92.18Financial Calculator MethodCompute AnPVPMTn1/YFV500003000.675-642,300.03Compute RPVPMTn1/Y FV125,000 158-9051.92+/-+/-CPTCPT19ExampleBudget Appliances has a promotion on a washer- dryer combination selling for $1750. Buyers
12、will pay “no money down and no payments for six months”. The first of 12 equal monthly payments is required six months from the purchase date. What should the monthly payments be if Budget Appliances is to earn 15% compounded monthly on its account receivable during both the deferred period and the
13、repayment period? 20Solution0181798765monthRRRRR123412Number of paymentsAnAn(def)deferralperiodj=15% compoundedmonthly p=i=j/m=1.25% n=12 d=5 An(def)=$1750Purchasedate21Financial calculator methodStep 1: calculate An .Step 2:calculate Rp=1.25% d=5 An(due)=$1750PVPMTn+/-051862.14FV17501/Y1.25PVPMTn+/-012 168.07FVR=$168.07CPTCPT22
