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Determining Ordinary Annuity Payments Determine the amount of the periodic payments needed to pay off the following purchases. Payments are made at the end of the period. 1. 2. Purchase of a flat-screen TV for $1,205. Monthly payments are to be made for one year with interest at 24% per annum, compounded monthly. Purchase of a waterskiing boat for $26,565. Quarterly payments are to be made for four years with interest at 8% per annum, compounded quarterly. 3.Purchase of a condominium for $65,500. Semiannual payments are to be made for with interest at 10% per annum, compounded semiannually. Choosing between Purchase Alternatives Foot Loose, Inc., needs to purchase a new shoelace-making machine. Machines Ready has agreed to sell Foot Loose the machine for $22,000 down and four payments of $5,700 to be paid in semiannual installments for the next two years. Do-It-Yourself Machines has offered to sell Foot Loose a comparable machine for $10,000 down and four semiannual payments of $9,000. If the current interest rate is 16%, compounded semiannually, which machine should Foot Loose purchase? Computing Mortgage Payments with the Use of Formulas George and Barbara Shrub would like to purchase a large white house and are evaluating their financing options. Bank A offers a mortgage at 12% annual interest, compounded monthly, with payments made at the end of each month. Bank B is offering a mortgage at 13% annual interest, compounded annually, with payments made at the end of each year. The purchase price of the white house is $250,000. 1.Use formulas to compute the following amounts: 1 (a)The monthly payment for the Bank A mortgage 2 (b)The annual payment for the Bank B mortgage 2. Which financing alternative would you advise the Shrubs to select? Determining Ordinary Annuity Payments Determine the amount of the periodic payments needed to pay off the following purchases. Payments are made at the end of the period. 1. Purchase of a flat-screen TV for $1,205. Monthly payments are to be made for one year with interest at 24% per annum, compounded monthly. So Monthly Payment = PMT(rate,nper,pv) = PMT(24%/12,12,1205) = $114 2. Purchase of a waterskiing boat for $26,565. Quarterly payments are to be made for four years with interest at 8% per annum, compounded quarterly. So Qtrly Payment = PMT(rate,nper,pv) = PMT(8%/4,4*4,26565) = $1957 3. Purchase of a condominium for $65,500. Semiannual payments are to be made for 10 years with interest at 10% per annum, compounded semiannually. So Monthly Payment = PMT(rate,nper,pv) = PMT(10%/2,10*2,65500) = $5256 Choosing between Purchase Alternatives Foot Loose, Inc., needs to purchase a new shoelace-making machine. Machines Ready has agreed to sell Foot Loose the machine for $22,000 down and four payments of $5,700 to be paid in semiannual installments for the next two years. Do-It-Yourself Machines has offered to sell Foot Loose a comparable machine for $10,000 down and four semiannual payments of $9,000. If the current interest rate is 16%, compounded semiannually, which machine should Foot Loose purchase? We calculate Present value of two machines. Foot Loose : Down payment 22000, Semi annual Payment PMT = $5700 No of payments nper = 4 So Present value = 22000 + PV(rate,nper,pmt) = 22000 + PV(16%/2,4,5700) = 22000 + $18,879 = $40,879 DIY machine : Down payment 10,000, Semi annual Payment PMT = $9000 No of payments nper = 4 So Present value = 10000 + PV(rate,nper,pmt) = 10000 + PV(16%/2,4,9000) = 10000+ $29,809 = $39,809 As PV of owning DIY machine is less. It should be purchased. Computing Mortgage Payments with the Use of Formulas Computing Mortgage Payments with the Use of Formulas George and Barbara Shrub would like to purchase a large white house and are evaluating their financing options. Bank A offers a 10- year mortgage at 12% annual interest, compounded monthly, with payments made at the end of each month. Bank B is offering a 10-year mortgage at 13% annual interest, compounded annually, with payments made at the end of each year. The purchase price of the white house is $250,000. 1.Use formulas to compute the following amounts: (a)The monthly payment for the Bank A mortgage Purchase price PV = 250,000, Rate = 12%/12 No of periods = 12*10 = 120 So Monthly payment = PMT(rate,nper,pv) = pmt(12%/12,120,250000) = $3,587 (b)The annual payment for the Bank B mortgage Purchase price PV = 250,000, Rate = 13% No of periods = 10 So Annual payment = PMT(rate,nper,pv) = pmt(13%,10,250000) =$46,072 2. Which financing alternative would you advise the Shrubs to select? Annual Payment in Option (a) = 12*3587 = 43041 Annual Payment in Option (b) = 46072 So Option (b), you pay an extra 46072-43041 = $3031 Hence Option (a) is better Determining Ordinary Annuity Payments Determine the amount of the periodic payments needed to pay off the following purchases. Payments are made at the end of the period. 1. Purchase of a flat-screen TV for $1,205. Monthly payments are to be made for one year with interest at 24% per annum, compounded monthly. So Monthly Payment = PMT(rate,nper,pv) = PMT(24%/12,12,1205) = $114 2. Purchase of a waterskiing boat for $26,565. Quarterly payments are to be made for four years with interest at 8% per annum, compounded quarterly. So Qtrly Payment = PMT(rate,nper,pv) = PMT(8%/4,4*4,26565) = $1957 3. Purchase of a condominium for $65,500. Semiannual payments are to be made for 10 years with interest at 10% per annum, compounded semiannually. So Monthly Payment = PMT(rate,nper,pv) = PMT(10%/2,10*2,65500) = $5256 Choosing between Purchase Alternatives Foot Loose, Inc., needs to purchase a new shoelace-making machine. Machines Ready has agreed to sell Foot Loose the machine for $22,000 down and four payments of $5,700 to be paid in semiannual installments for the next two years. Do-It-Yourself Machines has offered to sell Foot Loose a comparable machine for $10,000 down and four semiannual payments of $9,000. If the current interest rate is 16%, compounded semiannually, which machine should Foot Loose purchase? We calculate Present value of two machines. Foot Loose : Down payment 22000, Semi annual Payment PMT = $5700 No of payments nper = 4 So Present value = 22000 + PV(rate,nper,pmt) = 22000 + PV(16%/2,4,5700) = 22000 + $18,879 = $40,879 DIY machine : Down payment 10,000, Semi annual Payment PMT = $9000 No of payments nper = 4 So Present value = 10000 + PV(rate,nper,pmt) = 10000 + PV(16%/2,4,9000) = 10000+ $29,809 = $39,809 As PV of owning DIY machine is less. It should be purchased. Computing Mortgage Payments with the Use of Formulas Computing Mortgage Payments with the Use of Formulas George and Barbara Shrub would like to purchase a large white house and are evaluating their financing options. Bank A offers a 10- year mortgage at 12% annual interest, compounded monthly, with payments made at the end of each month. Bank B is offering a 10-year mortgage at 13% annual interest, compounded annually, with payments made at the end of each year. The purchase price of the white house is $250,000. 1.Use formulas to compute the following amounts: (a)The monthly payment for the Bank A mortgage Purchase price PV = 250,000, Rate = 12%/12 No of periods = 12*10 = 120 So Monthly payment = PMT(rate,nper,pv) = pmt(12%/12,120,250000) = $3,587 (b)The annual payment for the Bank B mortgage Purchase price PV = 250,000, Rate = 13% No of periods = 10 So Annual payment = PMT(rate,nper,pv) = pmt(13%,10,250000) =$46,072 2. Which financing alternative would you advise the Shrubs to select? Annual Payment in Option (a) = 12*3587 = 43041 Annual Payment in Option (b) = 46072 So Option (b), you pay an extra 46072-43041 = $3031 Hence Option (a) is better