Personal Finance Chapter 2 - Applying Time Value Concepts - PDF

Personal Finance Fifth Canadian Edition Applying Time Value Concepts Chapter 2 Copyright © 2022 Pearson Canada Inc. 2-1 Why is a Dollar today worth more than a Dollar tomorrow? Copyright © 2022 Pearson Canada In...

Personal Finance Fifth Canadian Edition Applying Time Value Concepts Chapter 2 Copyright © 2022 Pearson Canada Inc. 2-1 Why is a Dollar today worth more than a Dollar tomorrow? Copyright © 2022 Pearson Canada Inc. 2-2 Copyright © 2022 Pearson Canada Inc. 2-3 © 2024 The New York State & Local Retirement System —New York State Office of the State Comptroller Copyright © 2022 Pearson Canada Inc. 2-4 Chapter #2 Learning Objectives 1.Simple interest and compound interest. 2.Future value of a single dollar that you deposit today. 3.Present value of a single dollar amount that will be received in the future. 4.Future value of an annuity (a series of regular payments). 5.Present value of an annuity (a series of regular payments). Copyright © 2022 Pearson Canada Inc. 2-5 The Importance of the Time Value of Money The time value of money is especially important for estimating how your money may grow over time. Interest: the rent charged for the use of money (you will either pay or receive interest). Two ways of computing interest: simple interest (interest amount paid out to you each year) and compound interest (interest is re-invested back into the GIC). Copyright © 2022 Pearson Canada Inc. 2-6  Simple Interest (interest amount paid out to you each year) Copyright © 2022 Pearson Canada Inc. 2-7 Copyright © 2022 Pearson Canada Inc. 2-8 Simple Interest Formula At the end of each year, the bank will credit Farah’s chequing account with $30. The interest is NOT re- invested into the principal investment (a GIC) each year. Period Principal Interest Accumulated Amount Credited to (Annually) (a GIC) Earned (3%) Interest Chequing Account 1 $1000 $30 $30 $30 2 1000 30 60 30 3 1000 30 90 30 Copyright © 2022 Pearson Canada Inc. 2-9 PRACTICE QUESTION TRUE or FALSE With simple interest, the interest earned or paid is not reinvested. Answer: ???? Copyright © 2022 Pearson Canada Inc. 2 - 10 PRACTICE QUESTION TRUE or FALSE With simple interest, the interest earned or paid is not reinvested. Answer: TRUE Copyright © 2022 Pearson Canada Inc. 2 - 11  Compound Interest (interest is re-invested back into the GIC). Copyright © 2022 Pearson Canada Inc. 2 - 12  Compound Interest (The process of earning interest on interest) EXAMPLE: Farah decides to invest her money into a GIC that pays 3 percent interest compounded annually. Interest earned will be re-invested back into the GIC and not to her chequing account. Farah will earn interest on interest (compound interest). Period Accumulated (Annually) Principal Interest (3%) Interest Account Balance 1 $1000 $30 $30 $1030.00 2 1030 30.90 60.90 1060.90 3 1060.90 31.83 92.73 1092.73 Copyright © 2022 Pearson Canada Inc. 2 - 13 Copyright © 2022 Pearson Canada Inc. 2 - 14 Compounding Periods Interest can compound annually, or more frequently, such as semi-annually, quarterly, monthly, weekly, and daily periods. Compounding Period Number of Compounding Periods per Year (n) Annually (every year) 1 Semi-annually (every 6 months) 2 Quarterly (every 3 months) 4 Monthly (every month) 12 Weekly (every week) 52 Daily (every day) 365 Copyright © 2022 Pearson Canada Inc. 2 - 15 Practice Question TRUE or FALSE Compound interest means earning interest on interest. Answer: ??? Copyright © 2022 Pearson Canada Inc. 2 - 16 Practice Question TRUE or FALSE Compound interest means earning interest on interest. Answer: TRUE Copyright © 2022 Pearson Canada Inc. 2 - 17 Practice Question Jan wants to purchase a three-year GIC and has two options regarding interest income. The interest on GIC #1 is compounded every 6 months. The interest of GIC #2 compounds monthly. All interest payments are automatically reinvested back into the GIC. At the end of three years, which GIC will be worth more? a. GIC #1, or b. GIC #2? Copyright © 2022 Pearson Canada Inc. 2 - 18 Practice Question Jan wants to purchase a three-year GIC and has two options regarding interest income. The interest on GIC #1 is compounded every 6 months. The interest of GIC #2 compounds monthly. All interest payments are automatically reinvested back into the GIC. At the end of three years, GIC #2 will be worth more because it has more compounding period than GIC #1. Copyright © 2022 Pearson Canada Inc. 2 - 19 Future Value of a Single Dollar Amount Copyright © 2022 Pearson Canada Inc. 2 - 20 Using A Financial Calculator (1 of 2) Basic TVM function keys are located in the 3 rd row of the TI BA II Plus keyboard. Important to clear the existing TVM values in the calculator’s TVM worksheet each time! Enter a value for four of the five TVM keys (N, I/Y, PV, PMT, FV). CPT= compute key, used after all values inputted. Copyright © 2022 Pearson Canada Inc. 2 - 21 Using A Financial Calculator (2 of 2) Cash outflows, such as an investment amount, are entered as a negative number. Cash inflows, such as investment income, are entered as a positive number. Specify the number of payments per year (P/Y) and the number of compounding periods per year (C/Y) (press 2ND P/Y - default is 1 payment/year). Copyright © 2022 Pearson Canada Inc. 2 - 22 Future Value of a Single Dollar Amount – Using a Financial Calculator You have $5687 to invest in the stock market today. You expect a return of 10% compounded annually. How much will you have in 12 years? Determine: Number of periods=?? Interest rate per year=?? Present Value= ?? PMTs Made during the 12 years=0 Calculate FV Copyright © 2022 Pearson Canada Inc. 2 - 23 Future Value of a Single Dollar Amount – Using a Financial Calculator You have $5687 to invest in the stock market today. You expect a return of 10% compounded annually. How much will you have in 12 years? ANSWER: N=12, Interest/yr=10, PV=- 5687, PMT=0, CPT FV=$17,848.24. Copyright © 2022 Pearson Canada Inc. 2 - 24 PRACTICE QUESTION-Calculate the Future Value of a Single Dollar Amount Using your calculator, determine the future value of $5,000 invested at 9%, with interest compounded annually, for five years. A) 7,233 B) 7,693 C) 8,234 D) 8,325 Answer: ???? Determine PV=??, Interest Rate=??, Number of Periods=???, Then CPT FV. Copyright © 2022 Pearson Canada Inc. 2 - 25 PRACTICE QUESTION-Calculate the Future Value of a Single Dollar Amount Determine the future value of $5,000 invested at 9%, compounded annually for five years. A) 7,233 B) 7,693 C) 8,234 D) 8,325 Answer: B) PV=$5,000, Interest =9%, N=5, CPT, FV=$7,693 Copyright © 2022 Pearson Canada Inc. 2 - 26 PRACTICE QUESTION-Calculate the Future Value of a Single Dollar Amount Ben Collins plans to buy his first house for $ 230,000. If the property is expected to increase in value by 7 percent each year, what will the approximate house value be five years from now? Copyright © 2022 Pearson Canada Inc. 2 - 27 PRACTICE QUESTION - Continued Ben Collins plans to buy his first house for $ 230,000. If the property is expected to increase in value by 7 percent each year, what will the approximate house value be five years from now? Solution N 5, I/Y 7, PV -230000, PMT 0, CPT FV $322,586.90 Copyright © 2022 Pearson Canada Inc. 2 - 28 PRACTICE QUESTION-Calculate the Future Value of a Single Dollar Amount Joan Collins plans to buy her first house for $ 275,000. If the property is expected to increase in value by 5 percent each year, what will the approximate house value be seven years from now? Copyright © 2022 Pearson Canada Inc. 2 - 29 PRACTICE QUESTION-Calculate the Future Value of a Single Dollar Amount-Solution Joan Collins plans to buy her first house for $ 275,000. If the property is expected to increase in value by 5 percent each year, what will the approximate house value be seven years from now? Solution N 7, I/Y 5, PV – 275000, PMT 0, CPT FV 386952.62 Copyright © 2022 Pearson Canada Inc. 2 - 30 Present Value of a Single Dollar Amount Copyright © 2022 Pearson Canada Inc. 2 - 31 Present Value of a Single Dollar Amount – Using a Financial Calculator Loretta would like to accumulate $500 000 by the time she retires in 20 years. She can earn an 8.61% return compounded annually. How much must she invest today (as a one-time pay in)? Determine: N=??, Interest per year=??, FV=??, PMT=0 Copyright © 2022 Pearson Canada Inc. 2 - 32 Present Value of a Single Dollar Amount – Using a Financial Calculator Loretta would like to accumulate $500 000 by the time she retires in 20 years. She can earn an 8.61% return compounded annually. How much must she invest today? ANSWER: N=20, Interest per year=8.61%, FV=$500,000, PMT=0, Then CPT PV= $95,845.94. Copyright © 2022 Pearson Canada Inc. 2 - 33 PRACTICE QUESTION- Present Value of a Single Dollar Amount Approximately how much would you need to invest today, to receive $200 in ten years, if you received an annual interest rate of ten percent compounded annually? A) $65 B) $77 C) $87 D) $97 Answer: ???? Copyright © 2022 Pearson Canada Inc. 2 - 34 PRACTICE QUESTION- Present Value of a Single Dollar Amount Approximately how much would you need to invest today, to receive $200 in ten years, if you received an annual interest rate of ten percent compounded annually? A) $65 B) $77 C) $87 D) $97 Answer: B (FV=$200, Interest/Year=10%, N=10, CPT PV= $77) Copyright © 2022 Pearson Canada Inc. 2 - 35 PRACTICE QUESTION-Calculate the Present Value If you want to have $19,000 in ten years, how much would you have to deposit today if your investment earns a rate of 3 percent per annum? Copyright © 2022 Pearson Canada Inc. 2 - 36 PRACTICE QUESTION-Calculate the Present Value - Solution If you want to have $19,000 in ten years, how much would you have to deposit today if your investment earns a rate of 3 percent per annum? Solution N 10, I/Y 3, PMT 0 FV -19000, CPT PV 14137.78 Copyright © 2022 Pearson Canada Inc. 2 - 37 PRACTICE QUESTION-Calculate the Present Value If you want to have $18,000 in eight years, how much would you have to deposit today if your investment earns a rate of 3 percent per annum? Copyright © 2022 Pearson Canada Inc. 2 - 38 PRACTICE QUESTION-Calculate the Present Value - Solution If you want to have $18,000 in eight years, how much would you have to deposit today if your investment earns a rate of 3 percent per annum? Solution N 8, I/Y 3, PMT 0, FV -18000, CPT PV 14209.37 Copyright © 2022 Pearson Canada Inc. 2 - 39  ANNUITIES (Multiple Payments in One Year) Copyright © 2022 Pearson Canada Inc. 2 - 40 Compound Interest Time value of money is most commonly applied to two types of cash flows – a single dollar amount (a lump sum, which we just discussed above), and – an annuity Annuity: the payment of a series of equal cash flow payments at equal intervals of time. We will discuss annuities on the next set of slides. Copyright © 2022 Pearson Canada Inc. 2 - 41 Two Types of Annuities Ordinary annuity: a stream of equal payments that are received or paid at equal intervals in time at the end of a period. Annuity due: a series of equal cash flow payments that occur at the beginning of each period. **If the amount or frequency of the payment changes over time, the payment stream does not reflect an annuity. Copyright © 2022 Pearson Canada Inc. 2 - 42 Using Timelines The best way to illustrate the future value of an ordinary annuity or an annuity due is through the use of timelines. Timelines: diagrams that show payments received or paid over time. Copyright © 2022 Pearson Canada Inc. 2 - 43 Future Value of an Ordinary Annuity Copyright © 2022 Pearson Canada Inc. 2 - 44 Future Value of an Ordinary Annuity Example Timelines Copyright © 2022 Pearson Canada Inc. 2 - 45 Future Value of an Ordinary Annuity – Using a Financial Calculator Betty wants to accumulate $1 million by the end of 20 years by making equal annual year-end deposits over the next 20 years. Assuming Betty can earn 10 percent compounded annually over this period, how much must she deposit at the end of each year? Copyright © 2022 Pearson Canada Inc. 2 - 46  Future Value of an Ordinary Annuity – Using a Financial Calculator Betty wants to accumulate $1 million by the end of 20 years by making equal annual year-end deposits over the next 20 years. Assuming Betty can earn 10 percent compounded annually over this period, how much must she deposit at the end of each year? Solution FV=$1 Million, N=20, I/Y=10%/year, PV=), CPT PMT=$17,460. Copyright © 2022 Pearson Canada Inc. 2 - 47 Future Value of an Ordinary Annuity – Using a Financial Calculator Raymond wants to save the college tuition fees his child will need in ten years by starting with a deposit of $6500 today and depositing another $500 at the end of each year. How much will Raymond have in ten years if he gets a rate of return of four percent compounded annually? Copyright © 2022 Pearson Canada Inc. 2 - 48  Future Value of an Ordinary Annuity – Using a Financial Calculator Raymond wants to save the college tuition fees his child will need in ten years by starting with a deposit of $6500 today and depositing another $500 at the end of each year. How much will Raymond have in ten years if he gets a rate of return of four percent compounded annually? Solution N=10, PV=$6,500, PMT=$500, I/Y=4%, CPT FV=$15,625. Copyright © 2022 Pearson Canada Inc. 2 - 49 Future Value of an Annuity Due Copyright © 2022 Pearson Canada Inc. 2 - 50 Future Value of an Annuity Due (1 of 3) The diagram above reflects the cash flows that would be paid from an annuity due. Copyright © 2022 Pearson Canada Inc. 2 - 51 Future Value of an Annuity Due – Using a Financial Calculator Tamara decides to save $200 per month at the beginning of each month. The account pays an interest rate of 3% compounded annually. How much will be in the account in 2 years? Determine: First, Set calculator to the beginning of the month: N=??, Interest per year=3%/12, PV=0, PMT=$200, FV= ?? Copyright © 2022 Pearson Canada Inc. 2 - 52 Future Value of an Annuity Due – Using a Financial Calculator Tamara decides to save $200 per month at the beginning of each month. The account pays an interest rate of 3% compounded annually. How much will be in the account in 2 years? Determine: Set to Beginning of the month, p/y=12, N=24, Interest per period =3%, PV=0, PMT=$200, FV= $4,953 (Then reset calculator back to the end of Copyright © 2022 Pearson Canada Inc. 2 - 53 the period) Present Value of an Ordinary Annuity Copyright © 2022 Pearson Canada Inc. 2 - 54 Present Value of an Annuity The present value of an annuity can be obtained by discounting the individual cash flows of the annuity and totaling them. Copyright © 2022 Pearson Canada Inc. 2 - 55 Present Value of an Ordinary Annuity (1 of 6) Referring to our earlier example: Copyright © 2022 Pearson Canada Inc. 2 - 56 Present Value of an Ordinary Annuity What is the present value of an ordinary annuity paying $1550 each year for 15 years, with an interest rate of 6.6 percent per annum? Copyright © 2022 Pearson Canada Inc. 2 - 57 Present Value of an Ordinary Annuity What is the present value of an ordinary annuity paying $1550 each year for 15 years, with an interest rate of 6.6 percent per annum? Solution PMT=$1,550, N=15, I/Y=6.6%, FV=0, CPT PV=$14,481 Copyright © 2022 Pearson Canada Inc. 2 - 58 Present Value of an Ordinary Annuity Example Selena wants to have enough funds to cover $13, 000 per year for four years of her daughter's university expenses and will need the money at the beginning of each year. If her funds get an annual return of 4.3 percent, how much would she need to have in the account when her daughter starts university? Copyright © 2022 Pearson Canada Inc. 2 - 59 Present Value of an Ordinary Annuity Example Selena wants to have enough funds to cover $13, 000 per year for four years of her daughter's university expenses and will need the money at the beginning of each year. If her funds get an annual return of 4.3 percent, how much would she need to have in the account when her daughter starts university? Solution BEGIN, PMT=$13,000, Y/I=4.3%, N=4, FV=0, CPT PV=$48,872. Copyright © 2022 Pearson Canada Inc. 2 - 60 Interest Rate Conversion Equivalent effective interest rates for various nominal interest rates: Nominal Interest Rate Effective Interest Rate a. 10% compounded annually 10.00% b. 10% compounded semiannually 10.25 c. 10% compounded quarterly 10.38 d. 10% compounded monthly 10.47 e. 10% compounded weekly 10.51 f. 10% compounded daily 10.52 Copyright © 2022 Pearson Canada Inc. 2 - 61 Practice Question What annual payment is required to pay off a three-year, $14,000 loan if the interest rate being charged is 6 percent? Copyright © 2022 Pearson Canada Inc. 2 - 62 Practice Question - Solution What annual payment is required to pay off a three-year, $14,000 loan if the interest rate being charged is 6 percent? Solution N 3, I/Y 6, PV 14000, FV 0, CPT= PMT 5237.54 Copyright © 2022 Pearson Canada Inc. 2 - 63  HOMEWORK Review Chapter #2 and review the TMV video that is posted in DC Connect for this lesson. Practice TVM questions for the textbook and slides. Copyright © 2022 Pearson Canada Inc. 2 - 64