VIEWS: 100 PAGES: 97 CATEGORY: Business POSTED ON: 6/22/2011
Fv = Future Value, Pv = Present Value, I = Interest Rate per Period, and N = Number of Periods document sample
Variables Variables Numbers and Variables Mgirvin uses Excel uses Formulas textbook uses Future Value FV FV ? FV or C Present Value PV PV 10000 PV or C Annual Interest Rate i 0.06 Number of compounding periods per year n 12 Years x 10 Period Rate i/n rate r Total Number of Periods x*n nper or npery t FV = PV*(1+i/n)^((x*n) FV(rate,nper,pmt,[pv],[type]) Total Interest Variables Variables Excel Numbers and Variables Mgirvin uses uses Formulas textbook uses Future Value FV FV ? FV or C Present Value PV PV 10000 PV or C Annual Interest Rate i 0.06 Number of compounding periods per year n 12 Years x 10 Period Rate i/n rate 0.005 r Total Number of Periods x*n nper or npery 120 t FV = PV*(1+i/n)^((x*n) $18,193.97 FV(rate,nper,pmt,[pv],[type]) $18,193.97 Total Interest $8,193.97 PV = Investment = $100.00 i = Annual Interest Rate = 0.1 n = Compounding Periods per Year = 1 x = years = 4 Simple Interest = Year Interest Earned Amount in Bank Year 0 Year 1 Year 2 Year 3 Year 4 FV = Future Value of Investment @ Simple Interest = PV = Investment = $100.00 i = Annual Interest Rate = 0.1 n = Compounding Periods per Year = 1 x = years = 4 Simple Interest = $10.00 Year Interest Earned Amount in Bank Year 0 $100.00 Year 1 $10.00 $110.00 Year 2 $10.00 $120.00 Year 3 $10.00 $130.00 Year 4 $10.00 $140.00 FV = Future Value of Investment @ Simple Interest = $140.00 PV = Investment = $100.00 i = Annual Interest Rate = 0.1 n = Compounding Periods per Year = 1 x = years = 4 Year Interest Earned Amount in Bank Year 0 Year 1 Year 2 Year 3 Year 4 FV = Future Value of Investment @ Compound Interest = FV = Future Value of Investment @ Compound Interest = FV = Future Value of Investment @ Simple Interest = FV = Future Value of Investment @ Compound Interest = Interest on Interest = PV = Investment = $100.00 i = Annual Interest Rate = 0.1 n = Compounding Periods per Year = 1 x = years = 4 Year Interest Earned Amount in Bank Year 0 $100.00 Year 1 $10.00 $110.00 Year 2 $11.00 $121.00 Year 3 $12.10 $133.10 Year 4 $13.31 $146.41 FV = Future Value of Investment @ Compound Interest = $146.41 FV = Future Value of Investment @ Compound Interest = $146.41 FV = Future Value of Investment @ Simple Interest = $140.00 FV = Future Value of Investment @ Compound Interest = $146.41 Interest on Interest = $6.41 PV = Investment = $100.00 i = Annual Interest Rate = 0.1 $300.00 Amount in Bank each Ye n = Compounding Periods per Year = 1 Amount in Bank each Ye $250.00 x = years = 4 $200.00 Amount in Bank each Year with Simple Amount in Bank each Year Time Interest with Compound Interest Difference $150.00 0 $100.00 $100.00 $0.00 1 $110.00 $110.00 $0.00 $100.00 2 $120.00 $121.00 $1.00 3 $130.00 $133.10 $3.10 $50.00 4 $140.00 $146.41 $6.41 5 $150.00 $161.05 $11.05 $0.00 6 $160.00 $177.16 $17.16 7 $170.00 $194.87 $24.87 8 $180.00 $214.36 $34.36 $700.00 9 $190.00 $235.79 $45.79 $600.00 10 $200.00 $259.37 $59.37 Future Value $500.00 $400.00 $300.00 $200.00 $100.00 $0.00 $300.00 Amount in Bank each Year with Compound Interest Amount in Bank each Year with Simple Interest $250.00 $200.00 $150.00 $100.00 $50.00 $0.00 0 1 2 3 4 5 6 7 8 9 10 $700.00 0.00% Annual Rate $600.00 $500.00 2.50% Annual Rate $400.00 5.00% Annual Rate $300.00 7.50% Annual Rate $200.00 10.00% Annual Rate $100.00 12.50% Annual Rate $0.00 15.00% Annual Rate 0 1 2 3 4 5 6 7 8 9 10 17.50% Annual Rate Time 20.00% Annual Rate If we invest $100,000.00 with an annual rate of 7.00% compounded 12 times a year for 10 years, what is the future value of the investment? Present Value = PV $ 100,000.00 Annual Interest Rate = i 7.00% Number of Compoundin Periods per Year = n 12 Years = x 10 Future Value = FV Period Rate = i/n Total Periods = n*x (1 + i/n)^(n*x) Future Value = FV Future Value = FV Future Value = FV Total Interest earned = cash put in - cash taken out Write it in words: If we invest $100,000.00 with an annual rate of 7.00% compounded 12 times a year for 10 years, what is the future value of the investment? Present Value = PV $ 100,000.00 Annual Interest Rate = i 7.00% Number of Compoundin Periods per Year = n 12 Years = x 10 Future Value = FV Period Rate = i/n 0.005833333 Total Periods = n*x 120 (1 + i/n)^(n*x) 2.0096613766956 Future Value = FV $ 200,966.14 Future Value = FV $ 200,966.14 Future Value = FV $200,966.14 Total Interest earned = cash put in - cash taken out $100,966.14 If we invest $100,000.00 with an annual rate of 7.00% compou times a year for 10 years, our future value of the investment $200,966.14. Of that amount, $100,966.14 is the interest earn Write it in words: investment. ual rate of 7.00% compounded 12 e value of the investment will be 66.14 is the interest earned on the ent. If we invest $15,000.00 with an annual rate of 5.50% compounded 365 times a year for 10 years, what is the future value of the investment? Present Value = PV $ 15,000.00 Annual Interest Rate = i 5.50% Number of Compoundin Periods per Year = n 365 Years = x 10 Future Value = FV Period Rate = i/n Total Periods = n*x Future Value = FV Future Value = FV Total Interest earned = cash put in - cash taken out Write it in words: If we invest $15,000.00 with an annual rate of 5.50% compounded 365 times a year for 10 years, what is the future value of the investment? Present Value = PV $ 15,000.00 Annual Interest Rate = i 5.50% Number of Compoundin Periods per Year = n 365 Years = x 10 Future Value = FV Period Rate = i/n 0.000150685 Total Periods = n*x 3650 Future Value = FV $ 25,997.72 Future Value = FV $25,997.72 Total Interest earned = cash put in - cash taken out $10,997.72 If we invest $15,000.00 with an annual rate of 5.50% compoun times a year for 10 years, our future value of the investment $25,997.72. Of that amount, $10,997.72 is the interest earned Write it in words: investment. al rate of 5.50% compounded 365 e value of the investment will be 7.72 is the interest earned on the ment. How much would we have to invest today, if we want to have $1,000,000.00 in 40 years and we could earn an annual interest rate (discount rate) of 10.00% compounded 12 times a year? Present Value = PV "Annual Interest Rate" = Discount Rate (term used when doing PV calculations) = i 10.00% Number of Compoundin Periods per Year = n 12 Years = x 40 Future Value = FV $ 1,000,000.00 Period Payment = PMT Period Rate = i/n Total Periods = n*x (1 + i/n)^(n*x) Present Value = PV Present Value = PV Present Value = PV Total Interest earned = cash put in - cash taken out Write it in words: How much would we have to invest today, if we want to have $1,000,000.00 in 40 years and we could earn an annual interest rate (discount rate) of 10.00% compounded 12 times a year? Present Value = PV "Annual Interest Rate" = Discount Rate (term used when doing PV calculations) = i 10.00% Number of Compoundin Periods per Year = n 12 Years = x 40 Future Value = FV $ 1,000,000.00 Period Payment = PMT Period Rate = i/n 0.008333333 Total Periods = n*x 480 (1 + i/n)^(n*x) 53.7006631743289 Present Value = PV $ 18,621.74 Present Value = PV $ 18,621.74 Present Value = PV -$18,621.74 Total Interest earned = cash put in - cash taken out $ 981,378.26 We would have to invest $18,621.74 today, if we want t $1,000,000.00 in 40 years and we could earn an annual int Write it in words: (discount rate) of 10.00% compounded 12 times a y ��������=��������(1+����/����)^(����∗����) ��������/((1+����/����)^(����∗����))=(��������(1+����/����)^(����∗����))/((1+���� /����)^(����∗����)) ��������/((1+����/����)^(����∗����))=(��������(1+����/����)^(����∗����))/((1+���� /����)^(����∗����)) ��������/((1+����/����)^(����∗����))=�������� ould have to invest $18,621.74 today, if we want to have 00.00 in 40 years and we could earn an annual interest rate count rate) of 10.00% compounded 12 times a year. How much would we have to invest today, if we want to have $150,000.00 (for our daughter's college tuition) in 18 years and we could earn an annual interest rate (discount rate) of 6.95% compounded 365 times a year? Present Value = PV "Annual Interest Rate" = Discount Rate (term used when doing PV calculations) = i 6.95% Number of Compoundin Periods per Year = n 365 Years = x 18 Future Value = FV $ 150,000.00 Period Payment = PMT Period Rate = i/n Total Periods = n*x (1 + i/n)^(n*x) Present Value = PV Present Value = PV Present Value = PV Total Interest earned = cash put in - cash taken out Write it in words: How much would we have to invest today, if we want to have $150,000.00 (for our daughter's college tuition) in 18 years and we could earn an annual interest rate (discount rate) of 4.00% compounded 365 times a year? Present Value = PV "Annual Interest Rate" = Discount Rate (term used when doing PV calculations) = i 4.00% Number of Compoundin Periods per Year = n 365 Years = x 18 Future Value = FV $ 150,000.00 Period Payment = PMT Period Rate = i/n 0.000109589041095890 Total Periods = n*x 6570 (1 + i/n)^(n*x) 2.0543521665502 Present Value = PV $ 73,015.72 Present Value = PV $ 73,015.72 Present Value = PV ($73,015.72) Total Interest earned = cash put in - cash taken out $ 76,984.28 We would have to invest $73,015.72 today, if we want to (for our daughter's college tuition) in 18 years and we co Write it in words: interest rate (discount rate) of 4.00% compounded 36 e to invest $73,015.72 today, if we want to have $150,000.00 hter's college tuition) in 18 years and we could earn an annual e (discount rate) of 4.00% compounded 365 times a year? If you want to buy a $350,000.00 C & C Router Machine to improve manufacturing efficiency and you have $200,000.00 today that you can invest at an annual rate of 8.50% compounded 12 times a year, how long do you have to wait (be careful about what period you need to make the calculation and what period you need for the answer) until you can afford the machine? (Assume the $350,000.00 is the price in the future). PV $ 200,000.00 i 8.50% n 12 FV $ 350,000.00 x*n months x/n years Write it in words: 35 = 20*(1.0071)^(12*x) 35/20 = (1.0071)^(12*x) LN(35/20) = LN((1.0071)^(12*n)) LN(35/20) = 12*n*LN(1.0071) LN(35/20)/LN(1.0071) = 12*n LN(35/20)/LN(1.0071)/12 = n 6.6 = n = years 6.591550252 FV/PV 1.75 (1+i/n) 1.007083333333330 LN(FV/PV) 0.559615788 LN((1+i/n)) 0.007058364 LN(FV/PV)/LN((1+i/n)) 79.28406056 months 79.2840605560736/n = x = 6.607005046 years If you want to buy a $350,000.00 C & C Router Machine to improve manufacturing efficiency and you have $200,000.00 today that you can invest at an annual rate of 8.50% compounded 12 times a year, how long do you have to wait (be careful about what period you need to make the calculation and what period you need for the answer) until you can afford the machine? (Assume the $350,000.00 is the price in the future). PV $ 200,000.00 i 8.50% n 12 FV $ 350,000.00 x*n 79.28406056 months x/n 6.607005046 years If you have $200,000.00 to invest today at 8.50% compounded 12 a year and you Write it in words: need $350,000.00 to buy the machine, you would have to wait 6.607 years 35 = 20*(1.0071)^(12*x) 35/20 = (1.0071)^(12*x) LN(35/20) = LN((1.0071)^(12*n)) LN(35/20) = 12*n*LN(1.0071) LN(35/20)/LN(1.0071) = 12*n LN(35/20)/LN(1.0071)/12 = n 6.6 = n = years 6.591550252 FV/PV 1.75 (1+i/n) 1.007083333333330 LN(FV/PV) 0.559615788 LN((1+i/n)) 0.007058364 LN(FV/PV)/LN((1+i/n)) 79.28406056 months 79.2840605560736/n = x = 6.607005046 years nded 12 a year and you to wait 6.607 years The Higher The Discount Rate, The Lower The Present Value $120.00 $100.00 $80.00 0.00% Annual Rate 2.50% Annual Rate Present Value 5.00% Annual Rate $60.00 7.50% Annual Rate 10.00% Annual Rate 12.50% Annual Rate 15.00% Annual Rate $40.00 17.50% Annual Rate 20.00% Annual Rate $20.00 $0.00 0 1 2 3 4 5 6 7 8 9 10 Time If you want to buy a $350,000.00 C & C Router Machine to improve manufacturing efficiency and you can invest $250,000.00 today for the next 5 years (compounding 2 times a year), what annual interest rate (APR) do you need to find (be careful about periods) so that you can afford the machine? (Assume the $350,000.00 is the price in the future). PV $ 250,000.00 n 2 x 5 FV $ 350,000.00 i/n i Write it in words: FV/PV 1.4 FV/PV^(1/(n*x)) 1.034219694 FV/PV^(1/(n*x))-1 0.034219694 Half year rate 0.0342196941293802*2 0.068439388 Annual Rate If you want to buy a $350,000.00 C & C Router Machine to improve manufacturing efficiency and you can invest $250,000.00 today for the next 5 years (compounding 2 times a year), what annual interest rate (APR) do you need to find (be careful about periods) so that you can afford the machine? (Assume the $350,000.00 is the price in the future). PV $ 250,000.00 n 2 x 5 FV $ 350,000.00 i/n 3.42% i 6.84% If you want to buy a $350,000.00 C & C Router Machine to improve manufacturing efficiency and you can invest $250,000.00 today for the next 5 years (compounding 2 times a year), the annual interest rate (APR) you need to Write it in words: find is 6.84%. FV/PV 1.4 FV/PV^(1/(n*x)) 1.034219694 FV/PV^(1/(n*x))-1 0.034219694 Half year rate 0.0342196941293802*2 0.068439388 Annual Rate Rule of 72 givens an estimate of what rate you need to double Money. PV $1,000.00 FV $2,000.00 n 12 x 5 n*x Notice that this is the number 1.2 not 0.012. To get an estimate of Rule of 72: i/n aprox = 72/(n*x) Rule of 72), you would have to divide the result by Notice that this is the number 14.4 not 0.144. To get an estimate of i = (72/(n*x)*n) = Rule of 72), you would have to divide the result by estimate of rate needed to double $ Using RATE: i check FV check Remember, this is an estimate. not 0.012. To get an estimate of the real rate (using the would have to divide the result by 100. not 0.144. To get an estimate of the real rate (using the would have to divide the result by 100. Rule of 72 givens an estimate of what rate you need to double Money. PV $1,000.00 FV $2,000.00 n 12 x 5 n*x 60 Notice that this is the number 1.2 not 0.012. To get an estimate of the re Rule of 72: i/n aprox = 72/(n*x) 1.200 Rule of 72), you would have to divide the result by 100 Notice that this is the number 14.4 not 0.144. To get an estimate of the r i = (72/(n*x)*n) = 14.40 Rule of 72), you would have to divide the result by 100 estimate of rate needed to double $ 0.144 Using RATE: 13.94% i check FV check $2,045.65 Remember, this is an estimate. To get an estimate of the real rate (using the to divide the result by 100. To get an estimate of the real rate (using the to divide the result by 100. What is the Annual Interest Rate? Time Given as: 36 months # of Compounding Periods per Year n 2 Present Value PV 72,500.00 Future Value FV 100,000.00 Years x Total periods n*x Annual Interest Rate i Period Interest Rate i/n Check: What is the Annual Interest Rate? Time Given as: 36 months # of Compounding Periods per Year n 2 Present Value PV 72,500.00 Future Value FV 100,000.00 Years x 3 Total periods n*x 6 Annual Interest Rate i 11.012% Period Interest Rate i/n 5.506% Check: $100,000.00 If we invest $250,000.00 with an annual rate of 5.50% compounded 2 times a year for 15 years, what is the future value of the investment? Present Value = PV -$250,000.00 Annual Interest Rate = i 5.50% Number of Compoundin Periods per Year = n 2 Years = x 15 Future Value = FV Period Rate = i/n Total Periods = n*x Future Value = FV If we borrow $250,000.00 with an annual rate of 5.50% compounded 2 times a year for 15 years, what is the future value of the amount we owe? Present Value = PV $ 250,000.00 Annual Interest Rate = i 5.50% Number of Compoundin Periods per Year = n 2 Years = x 15 Future Value = FV Period Rate = i/n Total Periods = n*x Future Value = FV Check: $564,150.43 Check: ($564,150.43) If we invest $250,000.00 with an annual rate of 5.50% compounded 2 times a year for 15 years, what is the future value of the investment? Present Value = PV -$250,000.00 Annual Interest Rate = i 5.50% Number of Compoundin Periods per Year = n 2 Years = x 15 Future Value = FV Period Rate = i/n 0.0275 Total Periods = n*x 30 Future Value = FV $564,150.43 If we borrow $250,000.00 with an annual rate of 5.50% compounded 2 times a year for 15 years, what is the future value of the amount we owe? Present Value = PV $ 250,000.00 Annual Interest Rate = i 5.50% Number of Compoundin Periods per Year = n 2 Years = x 15 Future Value = FV Period Rate = i/n 0.0275 Total Periods = n*x 30 Future Value = FV -$564,150.43 Check: $564,150.43 Check: ($564,150.43) 4.1 4.2 4.3 PV = 1000 Age = 19 PV = $ 1.00 i= 8.00% Future Age = 25 n= 1 n= 1 Age Difference = x = x= 12 x= 4 FV = $ 100,000.00 FV = $ 2.00 FV = i= 11.00% i= FV = n= 1 i= x= Check with Rule of 72 PV = PV = 4.4 PV = $ 10,000.00 i= 7.00% n= 1 FV = $ 20,000.00 x= x= 4.4 PV = $ 10,000.00 i= 7.00% n= 1 FV = $ 30,000.00 n*x = x= 4.1 4.2 4.3 PV = 1000 Age = 19 PV = $ 1.00 i= 8.00% Future Age = 25 n= 1 n= 1 Age Difference = x = 6 x= 12 x= 4 FV = $ 100,000.00 FV = $ 2.00 FV = $ 1,360.49 i= 11.00% i= 5.95% FV = $1,360.49 n= 1 i= 5.95% x= 6 Check with Rule of 72 6 PV = 53464.08361 PV = ($53,464.08) FV = PV*(1+i/n)^(n*x) 2 = 1*(1+i)^12 2 = (1+i)^12 2^(1/12)-1 = i 4.4 PV = $ 10,000.00 i= 7.00% n= 1 FV = $ 20,000.00 x= 10.24476835 x= 10.24476835 4.4 PV = $ 10,000.00 i= 7.00% n= 1 FV = $ 30,000.00 n*x = 16.23757367 x= 16.23757367 FV = PV*(1+i/n)^(n*x) 2 = 1.07^x LN2/LN1.07 = x FV = PV*(1+i/n)^(n*x) 3 = 1.07^x LN3/LN1.07 = x 4.1 4.2 4.3 4.1 4.2 4.3 Compounding is a means to get rich, as long as you have prudent saving habits. The definition of Compounding is: "The process of accumulating interest in an investment over time to earn more interest." Discounting is like "interest backwards". If you know a future value amount and you want to know what it is worth today, given an appropriate discount rate (same as interest rate), you make a Present Value calculation (PV = FV/((1+i/n)^(n*x))). The Present Value calculation is the Future Value calculation, but backwards. With the Future Value calculation you add all the interest to the Present Value amount to get the Future Value amount; time is going forward. However, with the Present Value calculation you take out (remove) all the interest from the Future Value amount to get the Present Value amount; time is going Backwards. The definition of Discounting is: "Using the appropriate discount rate, you discount back the future value amount to get the Present Value amount" or "what is the current value of future cash flows given an appropriate discount rate". As you increase the length of time involved in a future value calculation (assuming a positive rate of return), the future value increases or the present value decreases. The time variable, or "input", is the most important variable in the Future Value and Present Value calculations because it has the most effect on the resultant number as compared to the other input variables. As you increase the Period Interest Rate, i/n, the Future Value amount increases; whereas, the Present Value will decrease. 1st City 2nd City i 0.07 i 0.08 n 1 PV 8000 PV 8000 x 10 x 10 FV FV FV 1st City FV 2nd City FV Extra Interest Due To Compounding 1st City 2nd City i 0.07 i 0.08 n 1 PV 8000 PV 8000 x 10 x 10 FV $13,600.00 FV $17,271.40 FV $17,271.40 1st City FV $13,600.00 2nd City FV $17,271.40 Extra Interest Due To Compounding $3,671.40 textbook answer looks incorrect. Annual Interest # Compound No. PV Years Rate Periods FV 1 $ 3,150.00 6 18.00% 1 2 $ 8,453.00 19 6.00% 1 3 $ 89,305.00 13 11.00% 1 4 $ 227,382.00 29 5.00% 1 FV Annual Interest # Compound No. PV Years Rate Periods FV 1 $ 3,150.00 6 18.00% 1 $ 8,503.60 2 $ 8,453.00 19 6.00% 1 $ 25,575.39 3 $ 89,305.00 13 11.00% 1 $ 346,796.33 4 $ 227,382.00 29 5.00% 1 $ 935,935.14 FV $8,503.60 $25,575.39 $346,796.33 $935,935.14 Annual Interest No. PV PV Years Rate 1 12 4.00% 2 4 9.00% 3 16 12.00% 4 21 11.00% # Compound Periods FV 1 $ 17,328.00 1 $ 41,517.00 1 $ 790,382.00 1 $ 647,816.00 Annual Interest No. PV PV Years Rate 1 ($10,823.02) $ 10,823.02 12 4.00% 2 ($29,411.69) $ 29,411.69 4 9.00% 3 ($128,928.43) $ 128,928.43 16 12.00% 4 ($72,388.42) $ 72,388.42 21 11.00% # Compound Periods FV 1 $ 17,328.00 1 $ 41,517.00 1 $ 790,382.00 1 $ 647,816.00 Annual Interest # Compound No. PV Years Rate Annual Interest Rate Periods 1 $ 715.00 6 1 2 $ 905.00 7 1 3 $ 15,000.00 18 1 4 $ 70,300.00 21 1 FV $ 1,381.00 $ 1,718.00 $ 141,832.00 $ 312,815.00 Annual Interest Annual Interest # Compound No. PV Years Rate Rate Periods 1 $ 715.00 6 11.60% 11.60% 1 2 $ 905.00 7 9.59% 9.59% 1 3 $ 15,000.00 18 13.29% 13.29% 1 4 $ 70,300.00 21 7.37% 7.37% 1 FV = PV*(1+i/n)^(n*x) 715 = 1381*(1+i/n)^(6) (715/1381)^(1/6)-1 FV $ 1,381.00 $ 1,718.00 $ 141,832.00 $ 312,815.00 Annual Interest # Compound No. PV Years Years Rate Periods 1 $ 250.00 9.00% 1 2 $ 1,941.00 7.00% 1 3 $ 32,805.00 12.00% 1 4 $ 32,500.00 19.00% 1 FV $ 1,105.00 $ 3,700.00 $ 387,120.00 $ 198,212.00 Annual Interest # Compound No. PV Years Years Rate Periods 1 $ 250.00 17.24506178 17.24506178 9.00% 1 2 $ 1,941.00 9.535063588 9.535063588 7.00% 1 3 $ 32,805.00 21.77872066 21.77872066 12.00% 1 4 $ 32,500.00 10.39415177 10.39415177 19.00% 1 FV $ 1,105.00 $ 3,700.00 $ 387,120.00 $ 198,212.00 Total Cost Education = FV = 320000 x= 18 PV = 50000 n= 1 i/n = i= Words: Total Cost Education = FV = 320000 x= 18 PV = 50000 n= 1 i/n = 10.8633% 10.8633% i= 0.108632935 0.108632935 To allow our current investment of $50,000.00 to cover the our child's eduction costs in Words: 18 years, we would have to earn an annual return of 10.86%. FV = PV*(1+i/n)^(n*x) (FV/PV)^(1/(n*x))-1 the our child's eduction costs in al return of 10.86%. Annual Rate = i = 0.07 FV = PV*(1+i/n)^(n*x) n= 1 LN(FV/PV)/LN(1+i/n) = n*x PV1 = 1 FV1 = 2 check FV check x*n = x= Annual Rate = i = 0.07 n= 1 PV2 = 1 FV2 = 4 check FV check x*n = x= Words: Words: LN(1+i/n) = n*x Annual Rate = i = 0.07 n= 1 PV1 = 1 Annual Rate = i = 0.07 FV = PV*(1+i/n)^(n*x) n= 1 LN(FV/PV)/LN(1+i/n) = n*x PV1 = 1 FV1 = 2 check FV check x*n = 10.24477 10.24477 $2.00 x= 10.24477 Annual Rate = i = 0.07 n= 1 PV2 = 1 FV2 = 4 check FV check x*n = 20.48954 20.48954 $4.00 x= 20.48954 To double my investment at an Annual Rate of 7.00% I would ha Words: to invest for 10.24years. To quadruple my investment at an Annual Rate of 7.00% I wou Words: have to invest for 20.49years. LN(1+i/n) = n*x nnual Rate of 7.00% I would have 10.24years. an Annual Rate of 7.00% I would for 20.49years. Year 2 1893 Year 1 2009 Year Difference = x = PV = $1.00 FV = $6,450.00 n= 1 check i/n = i= Year 2 1893 Year 1 2009 Year Difference = x = 116 PV = $1.00 FV = $6,450.00 n= 1 check i/n = 7.855186% 0.078552 i= 0.07855186 Unfunded Pension Liability = FV = $ 750,000,000.00 Must be paid in = years = x = 25 Discount Rate = i = 0.08 n= 1 n*x = 25 i/n = 0.08 Present Value of Liabilitiy (Lump Sum Value today that stock Analysts can subtract from current firm market value worth) = PV = Words: check Unfunded Pension Liability = FV = $ 750,000,000.00 Must be paid in = years = x = 25 Discount Rate = i = 0.08 n= 1 n*x = 25 i/n = 0.08 Present Value of Liabilitiy (Lump Sum Value today that stock Analysts can subtract from current firm market value worth) = PV = ($109,513,428.68) The financial analyst would like to know what the f today so it can help them to calculate what the fi worth today. The Present Value of the future Unfun Words: $109,513,428.68. check 109,513,428.68 st would like to know what the future liability is worth elp them to calculate what the firm's market value is esent Value of the future Unfunded Pension Liability is $109,513,428.68. FV = Lottery value in future = 2,000,000.00 x= 80 n= 1 Discount Rate = 0.09 Check PV = Words: FV = Lottery value in future = 2,000,000.00 x= 80 n= 1 Discount Rate = 0.09 Check PV = ($2,027.26) 2027.263 The present value of this future Words; lottery payout is $2,027.26. Part 1 Part 2 PV = $5,000.00 PV = $5,000.00 i= 0.105 i= 0.105 n= 1 n= 1 x= 45 x= 35 FV = FV = Words: Check Check Part 1 Part 2 PV = $5,000.00 PV = $5,000.00 i= 0.105 i= 0.105 n= 1 n= 1 x= 45 x= 35 FV = $446,963.97 FV = $164,683.37 The investment Strategy that this suggests is that the most important variable in investment strategy is the Total Number of Periods. For 10 extra years, we get Words: $282,280.60 extra dollars of return. Check Check 446963.9694 164683.366 PV = 13000 Time Line x= 6 0 1 2 3 4 i= 0.09 $13,000.00 n= 1 FV = Words: Check: 5 6 7 8 years $21,802.30 PV = 13000 Time Line x= 6 0 1 2 3 4 i= 0.09 $13,000.00 n= 1 FV = $21,802.30 If we receive $21,802.30 in 2 years, and then we wait 6 years, our FV will be $21,802.30 Words: (Remember: 8 - 2 = 6). Check: 21802.3014 5 6 7 8 years $21,802.30 PV = 1 FV = 4 Months = 24 Years = x = n= 4 (3 month rate) , then 3 + 3 + 3 + 3 = 12 months n*x = i/n = <<== Three Month Rate Check: Check: i= <<== Annual Rate Words: PV = 1 FV = 4 Months = 24 Years = x = 2 n= 4 (3 month rate) , then 3 + 3 + 3 + 3 = 12 months, so 4 total period in a year n*x = 8 i/n = 18.921% <<== Three Month Rate Check: Check: i= 75.683% <<== Annual Rate 0.189207 4 First, if the problems gives us time in months, we have to determine the years. After we do that the problem is straight forward. The 3-month rate to Words: quadruple your investment would be 18.92% period in a year i/n = 0.35% n= 12 i= PV = $1,800.00 FV = $3,500.00 Check: n*x = months x= years Words: i/n = 0.35% n= 12 i= 0.042 PV = $1,800.00 FV = $3,500.00 Check: n*x = 190.3255241 months 190.3255 x= 15.86046034 years It would take 15.86 years for the investment to grow to $3,500.00 given a monthly Words: Rate of 0.35%. FV = $75,000.00 n= 12 i/n = 0.42% i= x= 10 n*x PV = Words: FV = $75,000.00 n= 12 i/n = 0.42% i= 5.040% x= 10 n*x 120 PV = ($45,356.05) Words: The Present Value of $75,000.00 given a monthly rate of 0.42% is $45,356.05. 1st 2nd FV = 1,000,000.00 FV = 1,000,000.00 x= 45 x= 45 i= 11.00% i= 5.00% n= 1 n= 1 PV = PV = Words: Check: Check: 1st 2nd FV = 1,000,000.00 FV = 1,000,000.00 x= 45 x= 45 i= 11.00% i= 5.00% n= 1 n= 1 PV = -9,129.90 PV = -111,296.51 I want to be a millionaire when I retire, so with either option, I am going to invest earlier in Words: life instead of later.