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1 Mathematics of Finance With a Financial Calculator Presentation 2 Compound Value Parameters: Interest rate (i) Amount that is invested, present value (PV) Time money remains invested (n) Future value of the investment in n years (FVn) Periodic equal payment (or deposit) (PMT) 3 Compound Value Future Value of a Lump Sum (one time payment): Value at some time in the future of an investment Interest compounds: earn interest on interest in later years. Future value in one year is present value plus the interest that is earned over the year. 4 Compound Value Future Value of a Lump Sum (one time payment): In General FVn = PV(1+ i)n 5 Compound Value Present Value of a Lump Sum (one time payment): Value today of an amount to be received or paid in the future. FVn PV = (1 + i)n Example: Expect to receive $100 in eight years. If can invest at 10%, what is it worth today? 6 Compound Value Present Value of a Lump Sum (one time payment): Value today of an amount to be received or paid in the future. FV8 PV = (1 + i)8 Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 1 2 3 4 5 6 7 8 ? $100 7 Compound Value Present Value of a Lump Sum (one time payment): Value today of an amount to be received or paid in the future. FV8 PV = (1 + i)8 Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 1 2 3 4 5 6 7 8 ? $100 8 Financial Calculator Setting Display Should show at least 2 decimal places on dollar 0.00 amounts and 4 decimal places on percentages P/YR N I/YR PV PMT FV CLEAR ALL INPUT 7 8 9 4 5 6 x 1 2 3 – BEG/END DISP 0 . = + HP10B Calculator 9 Financial Calculator Setting Display Should show at least 2 decimal places on dollar 0.00 amounts and 4 decimal places on percentages P/YR N I/YR PV PMT FV CLEAR ALL INPUT 7 8 9 4 5 6 x 1 1 2 3 – BEG/END DISP 0 . = + HP10B Calculator 10 Financial Calculator Setting Display Should show at least 2 decimal places on dollar 0.00 amounts and 4 decimal places on percentages P/YR N I/YR PV PMT FV CLEAR ALL INPUT 7 8 9 4 5 6 x 1 1 2 3 – 2 BEG/END DISP 0 . = + HP10B Calculator 11 Financial Calculator Setting Display Should show at least 2 decimal places on dollar 0.0000 amounts and 4 decimal places on percentages P/YR N I/YR PV PMT FV CLEAR ALL INPUT 3 7 8 9 4 5 6 x 1 1 2 3 – 2 BEG/END DISP 0 . = + HP10B Calculator 12 Financial Calculator Clearing Memory Financial calculators contain a number of memory 0.0000 registers. These registers should be cleared to P/YR prevent carry-over errors. N I/YR PV PMT FV CLEAR ALL INPUT 7 8 9 4 5 6 x 1 2 3 – BEG/END DISP 0 . = + HP10B Calculator 13 Financial Calculator Clearing Memory Financial calculators contain a number of memory 0.0000 registers. These registers should be cleared to P/YR prevent carry-over errors. N I/YR PV PMT FV CLEAR ALL INPUT 7 8 9 1 4 5 6 x 1 2 3 – BEG/END DISP 0 . = + HP10B Calculator 14 Financial Calculator Clearing Memory Financial calculators contain a number of memory 0.0000 registers. These registers should be cleared to P/YR prevent carry-over errors. N I/YR PV PMT FV 2 CLEAR ALL INPUT 7 8 9 1 4 5 6 x 1 2 3 – BEG/END DISP 0 . = + HP10B Calculator 15 Financial Calculator Setting Compounding Frequency Compounding should be set to annual, i.e. P/YR=1, not 0.0000 the factory setting of 12. P/YR N I/YR PV PMT FV CLEAR ALL INPUT 7 8 9 4 5 6 x 1 2 3 – BEG/END DISP 0 . = + HP10B Calculator 16 Financial Calculator Setting Compounding Frequency Compounding should be set to annual, i.e. P/YR=1, not 1.0000 the factory setting of 12. P/YR N I/YR PV PMT FV CLEAR ALL INPUT 7 8 9 1 4 5 6 x 1 2 3 – BEG/END DISP 0 . = + HP10B Calculator 17 Financial Calculator Setting Compounding Frequency Compounding should be set to annual, i.e. P/YR=1, not 1.0000 the factory setting of 12. P/YR N I/YR PV PMT FV CLEAR ALL INPUT 7 8 9 1 4 5 6 x 2 1 2 3 – BEG/END DISP 0 . = + HP10B Calculator 18 Financial Calculator Setting Compounding Frequency Compounding should be set to annual, i.e. P/YR=1, not 1.0000 the factory setting of 12. P/YR N I/YR PV PMT FV 3 CLEAR ALL INPUT 7 8 9 1 4 5 6 x 2 1 2 3 – BEG/END DISP 0 . = + HP10B Calculator 19 Financial Calculator Setting Compounding Frequency Compounding should be set to annual, i.e. P/YR=1, not 1 P/Yr the factory setting of 12. To check setting CLEAR the P/YR calculator (holding down the N I/YR PV PMT FV CLEAR ALL key) CLEAR ALL INPUT 2 7 8 9 1 4 5 6 x 1 2 3 – BEG/END DISP 0 . = + HP10B Calculator 20 Financial Calculator Solution Present Value of a Lump Sum (one time payment): Previous Example: Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 1 2 3 4 5 6 7 8 9 10 ? $100 Using Formula: 100 PV = (1+.1)8 = 46.65 21 Financial Calculator Solution Present Value of a Lump Sum (one time payment): Previous Example: Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 1 2 3 4 5 6 7 8 9 10 ? $100 8.0000 N I/YR PV PMT FV 8 22 Financial Calculator Solution Present Value of a Lump Sum (one time payment): Previous Example: Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 1 2 3 4 5 6 7 8 9 10 ? $100 10.000 N I/YR PV PMT FV Enter the Interest Rate as a WHOLE # 8 10 23 Financial Calculator Solution Present Value of a Lump Sum (one time payment): Previous Example: Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 1 2 3 4 5 6 7 8 9 10 ? $100 100.0000 N I/YR PV PMT FV 8 10 100 24 Financial Calculator Solution Present Value of a Lump Sum (one time payment): Previous Example: Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 1 2 3 4 5 6 7 8 9 10 ? $100 - 46.65 N I/YR PV PMT FV 8 10 ? 100 25 Compound Value Present Value of a Lump Sum (one time payment): Previous Example: Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 1 2 3 4 5 6 7 8 9 10 ? $100 Additional Calculator Notes: - 46.65 Can change any or all parameters without reentering others N I/YR PV PMT FV 8 10 100 26 Compound Value Present Value of a Lump Sum (one time payment): Previous Example: Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 1 2 3 4 5 6 7 8 9 10 ? $100 Additional Calculator Notes: 5.0000 Can change any or all parameters without reentering others Change Interest rate to N I/YR PV PMT FV 5% 8 10 100 5 27 Compound Value Present Value of a Lump Sum (one time payment): Previous Example: Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 1 2 3 4 5 6 7 8 9 10 ? $100 Additional Calculator Notes: - 67.68 Can change any or all parameters without reentering others Change Interest rate to N I/YR PV PMT FV 5% 8 10 ? 100 5 28 Compound Value Present Value of a Lump Sum (one time payment): Previous Example: Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 1 2 3 4 5 6 7 8 9 10 ? $100 Additional Calculator Notes: 0.0000 Can check the number entered in each memory location using the recall (RCL) key. N I/YR PV PMT FV RCL 29 Compound Value Present Value of a Lump Sum (one time payment): Previous Example: Example: Expect to receive $100 in EIGHT years. If can invest at 10%, what is it worth today? 0 1 2 3 4 5 6 7 8 9 10 ? $100 Additional Calculator Notes: 8.0000 Can check the number entered in each memory location using the recall (RCL) key. N I/YR PV PMT FV Check setting for years: RCL 30 Compound Value Solve for other parameters (I/YR) Given any three of the following: PV, FV, i and n, the fourth can be computed. 31 Compound Value Solve for other parameters (I/YR) Given any three of the following: PV, FV, i and n, the fourth can be computed. Example: A $200 investment has grown to $230 over two years. What is the ANNUAL return on this investment? 0 1 2 $200 $230 32 Compound Value Solve for other parameters (I/YR) Given any three of the following: PV, FV, i and n, the fourth can be computed. Example: A $200 investment has grown to $230 over two years. What is the ANNUAL return on this investment? 0 1 2 $200 $230 33 Compound Value Solve for other parameters (I/YR) Given any three of the following: PV, FV, i and n, the fourth can be computed. Example: A $200 investment has grown to $230 over two years. What is the ANNUAL return on this investment? 0 1 2 $200 $230 0.00 or FVn = PV(1+ i)n N I/YR PV PMT FV 34 Compound Value Solve for other parameters (I/YR) Given any three of the following: PV, FV, i and n, the fourth can be computed. Example: A $200 investment has grown to $230 over two years. What is the ANNUAL return on this investment? 0 1 2 $200 $230 2.00 or FVn = PV(1+ i)n N I/YR PV PMT FV 2 35 Compound Value Solve for other parameters (I/YR) Given any three of the following: PV, FV, i and n, the fourth can be computed. Example: A $200 investment has grown to $230 over two years. What is the ANNUAL return on this investment? 0 1 2 $200 $230 2.00 When Entering inflows n and outflows of cash, or FVn = PV(1+ i) enter as follows: (-) = cash outflow N I/YR PV PMT FV (+) = cash inflow 2 36 Compound Value Solve for other parameters (I/YR) Given any three of the following: PV, FV, i and n, the fourth can be computed. Example: A $200 investment has grown to $230 over two years. What is the ANNUAL return on this investment? 0 1 2 $200 $230 – 200.00 When Entering inflows n and outflows of cash, or FVn = PV(1+ i) enter as follows: (-) = cash outflow N I/YR PV PMT FV (+) = cash inflow 2 -200 37 Compound Value Solve for other parameters (I/YR) Given any three of the following: PV, FV, i and n, the fourth can be computed. Example: A $200 investment has grown to $230 over two years. What is the ANNUAL return on this investment? 0 1 2 $200 $230 230.00 or FVn = PV(1+ i)n N I/YR PV PMT FV 2 -200 230 38 Compound Value Solve for other parameters (I/YR) Given any three of the following: PV, FV, i and n, the fourth can be computed. Example: A $200 investment has grown to $230 over two years. What is the ANNUAL return on this investment? 0 1 2 $200 $230 7.24 or FVn = PV(1+ i)n N I/YR PV PMT FV 2 ? -200 230 39 Compound Value Solve for other parameters (N) Given any three of the following: PV, FV, i and n, the forth can be computed. Example: How long will it take for a $300 investment to grow to $500 if 6% annual interest is earned? 40 Compound Value Solve for other parameters (N) Given any three of the following: PV, FV, i and n, the forth can be computed. Example: How long will it take for a $300 investment to grow to $500 if 6% annual interest is earned? 0 1 N $300 $500 41 Compound Value Solve for other parameters (N) Given any three of the following: PV, FV, i and n, the forth can be computed. Example: How long will it take for a $300 investment to grow to $500 if 6% annual interest is earned? 0 1 N $300 $500 42 Compound Value Solve for other parameters (N) Given any three of the following: PV, FV, i and n, the forth can be computed. Example: How long will it take for a $300 investment to grow to $500 if 6% annual interest is earned? 0 1 N $300 $500 – 300.00 N I/YR PV PMT FV -300 43 Compound Value Solve for other parameters (N) Given any three of the following: PV, FV, i and n, the forth can be computed. Example: How long will it take for a $300 investment to grow to $500 if 6% annual interest is earned? 0 1 N $300 $500 500.00 N I/YR PV PMT FV -300 500 44 Compound Value Solve for other parameters (N) Given any three of the following: PV, FV, i and n, the forth can be computed. Example: How long will it take for a $300 investment to grow to $500 if 6% annual interest is earned? 0 1 N $300 $500 6.00 N I/YR PV PMT FV 6 -300 500 45 Compound Value Solve for other parameters (N) Given any three of the following: PV, FV, i and n, the forth can be computed. Example: How long will it take for a $300 investment to grow to $500 if 6% annual interest is earned? 0 1 N $300 $500 8.77 N I/YR PV PMT FV ? 6 -300 500 46 Non-Annual Compounding All equations and calculator solutions thus far have assumed compounding occurs ONCE a year. 47 Non-Annual Compounding All equations and calculator solutions thus far have assumed compounding occurs ONCE a year. Example: Deposit $1,000 at 10% nominal annual interest rate. How much will you have at end of 1 year? ANNUAL COMPOUNDING 0 1 $1,000 $1,000(1.1) $1,100 SEMI-ANNUAL COMPOUNDING 0 6 months 1 $1,000 48 Non-Annual Compounding All equations and calculator solutions thus far have assumed compounding occurs ONCE a year. Example: Deposit $1,000 at 10% nominal annual interest rate. How much will you have at end of 1 year? ANNUAL COMPOUNDING 0 1 $1,000 $1,000(1.1) $1,100 Earn 10%/2=5% SEMI-ANNUAL COMPOUNDING each compounding period 0 6 months 1 $1,000 $1,000(1.05) $1,050 49 Non-Annual Compounding All equations and calculator solutions thus far have assumed compounding occurs ONCE a year. Example: Deposit $1,000 at 10% nominal annual interest rate. How much will you have at end of 1 year? ANNUAL COMPOUNDING 0 1 $1,000 $1,000(1.1) $1,100 Earn 10%/2=5% SEMI-ANNUAL COMPOUNDING each compounding period 0 6 months 1 $1,000 $1,000(1.05) $1,050 $1,050(1.05) $1,102.50 50 Non-Annual Compounding All equations and calculator solutions thus far have assumed compounding occurs ONCE a year. When compounding more than once a year, must adjust formula i mn m = # of compounding FVn = PV(1+m) periods in a year 51 Non-Annual Compounding All equations and calculator solutions thus far have assumed compounding occurs ONCE a year. When compounding more than once a year, must adjust formula i mn m = # of compounding FVn = PV(1+m) periods in a year Example: Deposit $1,800 at 8% nominal annual interest rate, compounded quarterly. How much will you have at end of 3 years? 52 Financial Calculator Solutions Setting Compounding Frequency Calculator makes adjustments for differing 4.0000 compounding periods based on the setting of P/YR xP/YR P/YR For Quarterly compounding N I/YR PV PMT FV set P/YR = 4 3 CLEAR ALL INPUT 7 8 9 1 4 5 6 x 2 1 2 3 – BEG/END DISP 0 . = + HP10B Calculator 53 Financial Calculator Solutions Setting Compounding Frequency Calculator makes adjustments for differing 8.0000 compounding periods based on the setting of P/YR xP/YR P/YR For Quarterly compounding N I/YR PV PMT FV set P/YR = 4 I/YR/YR is automatically CLEAR ALL adjusted by the P/YR INPUT setting. 7 8 9 4 5 6 x 1 2 3 – BEG/END DISP 0 . = + HP10B Calculator 54 Financial Calculator Solutions Setting Compounding Frequency Calculator makes adjustments for differing 12.0000 compounding periods based on the setting of P/YR xP/YR P/YR For Quarterly compounding N I/YR PV PMT FV set P/YR = 4 I/YR/YR is automatically CLEAR ALL adjusted by the P/YR 3 INPUT setting. 7 8 9 To adjust N by P/YR enter 4 5 6 x the number of years on the xP/YR key. 1 2 3 – 2 BEG/END DISP 1 0 . = + HP10B Calculator 55 Non-Annual Compounding All equations and calculator solutions thus far have assumed compounding occurs ONCE a year. When compounding more than once a year, must adjust formula i mn m = # of compounding FVn = PV(1+m) periods in a year Example: Deposit $1,800 at 8% nominal annual interest rate, compounded quarterly. How much will you have at end of 3 years? P/Yr = 4 12.00 Enter Years using Shift [xP/YR] xP/YR P/YR combination N I/YR PV PMT FV 3 56 Non-Annual Compounding All equations and calculator solutions thus far have assumed compounding occurs ONCE a year. When compounding more than once a year, must adjust formula i mn m = # of compounding FVn = PV(1+m) periods in a year Example: Deposit $1,800 at 8% nominal annual interest rate, compounded quarterly. How much will you have at end of 3 years? P/Yr = 4 8.00 xP/YR P/YR N I/YR PV PMT FV 3 8 57 Non-Annual Compounding All equations and calculator solutions thus far have assumed compounding occurs ONCE a year. When compounding more than once a year, must adjust formula i mn m = # of compounding FVn = PV(1+m) periods in a year Example: Deposit $1,800 at 8% nominal annual interest rate, compounded quarterly. How much will you have at end of 3 years? P/Yr = 4 – 1800.00 xP/YR P/YR N I/YR PV PMT FV 3 8 -1800 58 Non-Annual Compounding All equations and calculator solutions thus far have assumed compounding occurs ONCE a year. When compounding more than once a year, must adjust formula i mn m = # of compounding FVn = PV(1+m) periods in a year Example: Deposit $1,800 at 8% nominal annual interest rate, compounded quarterly. How much will you have at end of 3 years? P/Yr = 4 2,282.84 xP/YR P/YR N I/YR PV PMT FV 3 8 -1800 ? 59 Financial Calculator Solutions Automatic Alternative Settings P/Yr = 4 Calculator make 2,282.84 compounding adjustments automatically based on xP/YR P/YR P/YR setting. N I/YR PV PMT FV 3 8 -1800 ? 60 Financial Calculator Solutions Automatic Alternative Settings P/Yr = 4 Calculator make 2,282.84 compounding adjustments automatically based on xP/YR P/YR P/YR setting. N I/YR PV PMT FV You can keep P/YR=1 and 3 8 -1800 ? make the adjustments to N and I/YR manually. Manual Advantage: should never P/Yr = 1 need to change P/YR, 2,282.84 therefore fewer errors on later problems. P/YR If change P/YR, always N I/YR PV PMT FV change back to 1 P/YR after 12 2 -1800 ? doing problem. 61 Future Value of an Annuity Annuity- string of deposits with constant value and fixed interval. 0 1 2 3 $0 $100 $100 $100 Compute FV3 How much would this account have in it at the end of 3 years if interest were earned at a rate of 8% annually? 62 Future Value of an Annuity Annuity- string of deposits with constant value and fixed interval. 0 1 2 3 $0 $100 $100 $100 Compute FV3 How much would this account have in it at the end of 3 years if interest were earned at a rate of 8% annually? 3.00 N I/YR PV PMT FV 3 63 Future Value of an Annuity Annuity- string of deposits with constant value and fixed interval. 0 1 2 3 $0 $100 $100 $100 Compute FV3 How much would this account have in it at the end of 3 years if interest were earned at a rate of 8% annually? 8.00 N I/YR PV PMT FV 3 8 64 Future Value of an Annuity Annuity- string of deposits with constant value and fixed interval. 0 1 2 3 $0 $100 $100 $100 Compute FV3 How much would this account have in it at the end of 3 years if interest were earned at a rate of 8% annually? –100.00 N I/YR PV PMT FV 3 8 -100 65 Future Value of an Annuity Annuity- string of deposits with constant value and fixed interval. 0 1 2 3 $0 $100 $100 $100 Compute FV3 How much would this account have in it at the end of 3 years if interest were earned at a rate of 8% annually? 324.64 NOTE: PV = 0 since the cashflow in time period 0 = $0 N I/YR PV PMT FV 3 8 -100 ? 66 Future Value of an Annuity Example Susan is able to save $980/yr for retirement. She makes these deposits at the end of each year. If she invests her savings at 12% compounded annually, how much will she have upon retirement in 45 years? 67 Future Value of an Annuity Example Susan is able to save $980/yr for retirement. She makes these deposits at the end of each year. If she invests her savings at 12% compounded annually, how much will she have upon retirement in 45 years? 0 1 2 3 44 45 $980 $980 $980 $980 $980 68 Future Value of an Annuity Example Susan is able to save $980/yr for retirement. She makes these deposits at the end of each year. If she invests her savings at 12% compounded annually, how much will she have upon retirement in 45 years? 0 1 2 3 44 45 $980 $980 $980 $980 $980 1,331,065.43 N I/YR PV PMT FV 45 12 -980 ? 69 Future Value of an Annuity Example #1a Susan will make equal quarterly payments totaling $980/yr for retirement. She makes these deposits at the end of each quarter. If she invests her savings at 12% compounded quarterly, how much will she have upon retirement in 45 years? 0 1 2 45 P/Yr = 1 $245 1,661,944.10 N I/YR PV PMT FV 180 3 -245 ? 70 Present Value of an Annuity How much would the following cash flows be worth to you today if you could earn 8% on your deposits? 0 1 2 3 $0 $100 $100 $100 71 Present Value of an Annuity How much would the following cash flows be worth to you today if you could earn 8% on your deposits? 0 1 2 3 $0 $100 $100 $100 $92.60 $100/(1.08) $100 / (1.08)2 $85.73 $100 / (1.08)3 $79.38 $257.71 257.71 N I/YR PV PMT FV 3 8 ? -100 72 Present Value of an Annuity Loan Amortization Borrow $1,000 today, how much would the annual payments be if you are required to repay in two years and the interest rate is 10%? –576.19 N I/YR PV PMT FV 2 10 1,000 ? 73 Present Value of an Annuity Example #1a Bob borrows $5,000 from his children to purchase a used car. He agrees to make payments at the end of each month for the next 5 years. If the interest rate on this loan is 6%, what is the amount of the payments? 74 Present Value of an Annuity Example #1a Bob borrows $5,000 from his children to purchase a used car. He agrees to make payments at the end of each month for the next 5 years. If the interest rate on this loan is 6%, what is the amount of the payments? 0 1 5 $5,000 75 Present Value of an Annuity Example #1a Bob borrows $5,000 from his children to purchase a used car. He agrees to make payments at the end of each month for the next 5 years. If the interest rate on this loan is 6%, what is the amount of the payments? 0 1 5 $5,000 –96.66 N I/YR PV PMT FV 60 0.5 5,000 ? 76 Present Value of an Annuity Example #1a Bob borrows $5,000 from his children to purchase a used car. He agrees to make payments at the end of each month for the next 5 years. If the interest rate on this loan is 6%, what is the amount of the payments? 0 1 5 $5,000 –96.66 N I/YR PV PMT FV 60 0.5 5,000 ? 77 Annuity Due Two Types of Annuities Ordinary Annuity - Payments (or deposits) occur at the end of the period 0 1 2 FV = $205 $0 $100 $100 Annuity Due - Payments (or deposits) occur at the beginning of the period 0 1 2 $100 $100 FV = ? Each payment (or deposit) for an annuity due earns one additional period interest. 78 Annuity Due Solving Annuity Due Annuity Due - Payments (or deposits) occur at the beginning of the period 0 1 2 $100 $100 FV = ? FV AD = FV (ordinary) (1+i) PV AD = PV (ordinary) (1+i) 79 0.00 – 215.25 BEGIN BEGIN P/YR N I/YR PV PMT FV N I/YR PV PMT FV 2 5 100 ? CLEAR ALL INPUT 7 8 9 4 5 6 x 1 1 2 3 – 2 BEG/END DISP 0 . = + 80 Additional Problems Problem #1 Compute the monthly payments on a 30 year mortgage for a $120,000 loan at 8% annual interest, compounded monthly. 81 Additional Problems Problem #2 You have determined that your budget will only allow you to make a $700 monthly mortgage payment. If interest rates are currently 6% and mortgage terms are typically 30 years, what price range home should you be searching for if your downpayment is $15,000?

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posted: | 7/2/2010 |

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Present Value Calculator document sample

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