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Unit 6 1) Use the simple interest formula method to find the future value of an ordinary annuity of $3,500 paid annually after three years at 3.9% annual interest. Find the total interest earned Future annuity value is $______________ 2) Harry Taylor plans to pay an ordinary annuity of $6,000 annually for ten years so he can take a year's sabbatical to study for a master's degree in business. The annual rate of interest is 3.8%. How much will Harry have at the end of three years? How much interest will he earn on the investment after three years? At the end of three years Harry will have $____________ 3) Which annuity earns more interest an annuity due of $250 quarterly for two years at 8% annual interest compounded quarterly, or an annuity due of $500 semiannually for two years at 8% annual interest compounded semiannually? Choose the correct answer below: A) The semiannual annuity yields more interest B) The semiannual and quarterly annuities yield equal interest C) The quarterly annuity yields more interest 4) What semiannual sinking fund payment would be required to yield $46,000 nine years from now? The annual interest rate is 6% compounded semiannually. The sinking fund payment is $___________. 5) What is the present value of an ordinary annuity with annual payments of $670 at 7% annual interest for 25 years? The present value of an ordinary annuity is $_________ 6) Janice and Terry Van Dyke have decided to establish a semiannual ordinary annuity of $4,000 for the next twenty years at 12% annual interest compounded semiannually. How much should they invest in a lump sum now to provide the stream of payments? They should invest $_________ Unit 7 Homework 1) The family budget is illustrated in the figure to the right. What is the total take home pay and what percent is allocated for transportation? The total take home pay is $_________ The percent of the take home pay allocated for transportation is _______% 2) Find the mean for the amounts: $17,484; $14,987; $13,521; $14,600; $18,580; $14,993. The mean for the amounts is $_____________ 3) Find the median for the scores 93, 69, 71, 86, 71, 95, 89, 74, 71, 89, 89, 96, 73, 75 The median is _____________ 4) Find the mode for the amounts; $17,371; $14,940, $13,512; $14,543; $18,540; $14,940. Select the correct choice below and fill in any answer boxes within your choice A) The mode(s) is/are $__________ B) There is no mode 5) 6) 7) 8) 9) 10) Unit 6 1) Use the simple interest formula method to find the future value of an ordinary annuity of $3,500 paid annually after three years at 3.9% annual interest. Find the total interest earned.$409.5 Future annuity value is $_3909.5______ Workings Simple interest formula=PRT P=$3500 R=0.039 T=3yrs I=3500 0.039 3=$409.5 FAV=P+I 3500+409.5=$3909.5 2) Harry Taylor plans to pay an ordinary annuity of $6,000 annually for ten years so he can take a year's sabbatical to study for a master's degree in business. The annual rate of interest is 3.8%. How much will Harry have at the end of three years? How much interest will he earn on the investment after three years? $692.664 At the end of three years Harry will have $ _18692.4________ Workings A= $6000 n=3 r=0.038 Future Val. of ordinary annuity= A (1+r) -1 r =6000{(1+0.038) - 1}/0.038 =6000{3.115} =$18692.664 Interest earned $18692.664- $(6000 3) =$692.664 3) Which annuity earns more interest an annuity due of $250 quarterly for two years at 8% annual interest compounded quarterly, or an annuity due of $500 semiannually for two years at 8% annual interest compounded semiannually? Choose the correct answer below: A is the correct answer A) The semiannual annuity yields more interest B) The semiannual and quarterly annuities yield equal interest C) The quarterly annuity yields more interest Workings Future value of annuity due=A (1+r) - 1 (1+r) r Annuity due of $250 quarterly for 2 years and 8% annual interest compounded quarterly n = 2*4=8 periods r=8/4= 2% per period=0.02 FVA=250{(1+0.02)- 1}/0.02 (1+0.02) =2508.5831.02 =2188.657 Interest=2188.657 - (250*8) = $188.657 Annuity due of$500 semiannually for 2 years and 8% annual interest compounded semiannualy n = 2*2=4 periods r=8/2= 4% per period=0.04 FVA=500{(1+0.04)- 1}/0.04 (1+0.04) =5004.2461.04 =2208.161 Interest=2208.161 - (500*4) = $208.161 4) What semiannual sinking fund payment would be required to yield $46,000 nine years from now? The annual interest rate is 6% compounded semiannually. The sinking fund payment is $_1964.60________. Workings FV=$46000 n =18periods r =0.03 semiannually A=? r = FV (1+r) -1 =46000{0.03/ (1.03) -1} =46000*{0.03/0.702} =46000*0.043 =$1964.60 5) What is the present value of an ordinary annuity with annual payments of $670 at 7% annual interest for 25 years? 6) The present value of an ordinary annuity is $ 7807.90______ Present value of an ordinary annuity=A 1 - (1+r) r A=$670 n =25 r= 0.07 PVA= 670 {1-(1+0.07)}/0.07 =67011.654 =7807.90 6) Janice and Terry Van Dyke have decided to establish a semiannual ordinary annuity of $4,000 for the next twenty years at 12% annual interest compounded semiannually. How much should they invest in a lump sum now to provide the stream of payments? They should invest $_60185.19________ A= $4000 n =40 periods r=0.06 Present value of ordinary annuity=4000 {1-(1+0.06)}/0.06 =4000 15.046 =$60185.19 Unit 7 Homework 1) The family budget is illustrated in the figure to the right. What is the total take home pay and what percent is allocated for transportation? The total take home pay is $2000________ The percent of the take home pay allocated for transportation is __12% Workings Total take home pay $720+$400+$80+$90+$80+$90+$150+$150+$240=$2000 Percent allocated for transportation ($240/$2000) 100=12% 2) Find the mean for the amounts: $17,484; $14,987; $13,521; $14,600; $18,580; $14,993. The mean for the amounts is $_15,694.17___________ Workings Mean= x = ($17,484+$14,987+$13,521+ $14,600+ $18,580+$14,993) /6 = 15,694.17 3) Find the median for the scores 93, 69, 71, 86, 71, 95, 89, 74, 71, 89, 89, 96, 73, 75 The median is _80.5____________ Workings 69, 71, 71, 71, 73, 74, 75, 86, 89, 89, 89, 93, 95, 96 (75+86) /2= 80.5 4) Find the mode for the amounts; $17,371; $14,940, $13,512; $14,543; $18,540; $14,940. Select the correct choice below and fill in any answer boxes within your choice A) The mode(s) is/are $_14940_________ B) C) There is no mode 5) Workings 7 students out of 20 scored below 80% (7/20)100=35% =35% 6) Workings Class interval $0 - $9.99 $10 - $19.99 $20 - $29.99 $30 - $39.99 $40 - $49.99 Tally //// //// //// /// //// / // //// Class frequency 10 8 6 2 4 7) Workings Mean = (22+28+ 15+20+20)/5= 21 Score x 22 28 15 20 20 Deviation from mean( x - ) 1 7 -6 -1 -1 Relative frequency 33.33% 26.67% 20% 6.67% 13.33% 8) Workings ATC Score x 32 21 29 23 15 Deviation from mean( x - ) 8 -3 5 -1 -9 Mean = (32+21+29+23+15)/5=24 Sum of squares = 64+9+25+1+81=180 ( x - ) 64 9 25 1 81 9) ACT Score x 24 31 30 27 23 Total Deviation from mean( x - ) -3 4 3 0 -4 Workings Mean = (24+31+30+27+23)/5=27 Standard deviation= (x ) -1 = (50 /5-1) = 12.5 =3.536 ( x - ) 9 16 9 0 16 50 10) Workings Range=maximum-minimum =20-6 =14days