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2.4.2.G1 Time Value of Money Math Advanced Level © Take Charge Today – June 2016 – Time Value of Money Math – Slide 1 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Simple Interest vs. Compound Interest 2.4.2.G1 Simple Interest Compound Interest Interest earned on the principal investment only Earning interest on the principal and on previous interest earned Example: You deposit $200 in a 18-month CD and let the money earn interest Example: you deposit $200 in a money market account that compounds interest quarterly Principal is the original amount of money invested or saved © Take Charge Today – June 2016 – Time Value of Money Math – Slide 2 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Simple Interest Equation: Step 1 Prt = I P Principal r t Interest Rate Time Period I Interest Earned $1,000 invested at 7% interest rate for 5 years 1,000 .07 5 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 3 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 350.00 2.4.2.G1 Simple Interest Equation: Step 2 P+I =FV P Principal I FV Interest Earned Future Value of Investment $1,000 invested at 7% interest rate for 5 years 1,000 350 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 4 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona $1,350 2.4.2.G1 Compound Interest Equations There are two methods for calculating compound interest Single deposit investment Periodic investments A single sum of money invested once at the beginning of the investment period Equal amounts of money are invested at regular intervals, such as yearly, monthly, or biweekly © Take Charge Today – June 2016 – Time Value of Money Math – Slide 5 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Compound Interest Equation – Single Deposit Investment FV = future value of investment P = principal or original balance r = interest rate expressed as a decimal n = number of times interest is compounded annually t = number of years $1,000 invested at 7% interest rate compounded annually for 5 years © Take Charge Today – June 2016 – Time Value of Money Math – Slide 6 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Compound Interest Equation – Periodic Investments of Equal Amounts FV = future value of investment P = periodic deposit amount r = interest rate expressed as a decimal n = number of times interest is compounded annually t = number of years $1,000 invested every year at 7% annual interest rate for 5 years © Take Charge Today – June 2016 – Time Value of Money Math – Slide 7 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Comparing Simple versus Compound Interest Simple Interest = $1,350.00 Compound Interest for a Single Deposit Investment = $1,402.55 Why are they different? By reinvesting the interest earned, the interest payment keeps growing as interest is compounded on interest © Take Charge Today – June 2016 – Time Value of Money Math – Slide 8 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Comparing Compound Interest on a Single Deposit versus Periodic Investments Compound Interest on a Single Deposit = $1,403.00 2.4.2.G1 Periodic Investments of Equal Amounts = $5,750.74 To make the most of your money, utilize compound interest and continue to invest! © Take Charge Today – June 2016 – Time Value of Money Math – Slide 9 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Compound Interest • Number of times interest is compounded has effect on return • Compounding more frequently equals higher returns $1,000 invested at 7% for 5 years Compounding Method Compounded how often? Amount Investment is Worth Daily Monthly Quarterly Semi-annually Annually 365 12 4 2 1 $1,419.02 $1,417.63 $1,414.78 $1,410.60 $1,402.55 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 10 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Let’s Compare: Compound Interest Equation – Single Deposit Investment 2.4.2.G1 $1,000 invested at 7% interest rate compounded annually for 5 years $1,000 invested at 7% interest rate compounded quarterly for 5 years Earned $12.23 more because the interest was compounded more frequently © Take Charge Today – June 2016 – Time Value of Money Math – Slide 11 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Let’s Compare: Compound Interest Equation – Periodic Investments 2.4.2.G1 $1,000 invested every year at 7% annual interest rate for 5 years $1,000 invested quarterly at 7% annual interest rate for 5 years Earned $17,950.87 more because you contributed to the account quarterly and the interest was compounded more frequently © Take Charge Today – June 2016 – Time Value of Money Math – Slide 12 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Smart Investing Every variable in the formula impacts the amount of your return Rule of Thumb: The higher the variable, the greater your return P = Principal The larger the principal investment, the greater your return R = Interest Rate The higher the interest rate, the greater your return N = # of Times Interest is Compounded per Year The more often the interest is compounded, the greater your return. T = Number of Years The longer you leave your money in the investment, the greater your return © Take Charge Today – June 2016 – Time Value of Money Math – Slide 13 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Smart Investing Which would you choose? An investment earning compound interest OR An investment earning simple interest Largest return © Take Charge Today – June 2016 – Time Value of Money Math – Slide 14 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Smart Investing Which would you choose? An investment earning an interest rate of 2% OR An investment earning an interest rate of 2.1% Largest return © Take Charge Today – June 2016 – Time Value of Money Math – Slide 15 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Smart Investing Which would you choose? An investment with an interest rate compounded monthly OR An investment with an interest rate compounded yearly Largest return © Take Charge Today – June 2016 – Time Value of Money Math – Slide 16 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice Activities Choose your practice method Practice calculating using the step-by-step method (basic calculator) Practice calculating by entering all variables into the formula (advanced calculator) © Take Charge Today – June 2016 – Time Value of Money Math – Slide 17 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Practice calculating using the step-by-step method (basic calculator) Use with Time Value of Money Math Practice – Basic Calculator Worksheet © Take Charge Today – June 2016 – Time Value of Money Math – Slide 18 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #1 Camila deposited $600.00 into a savings account one year ago. She has been earning 1.2% in annual simple interest. Complete the following calculations to determine how much Camila’s money is now worth. P 600.00 P 600.00 Step One: T R .012 1 Step Two: I 7.20 I 7.20 A 607.20 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 19 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #1 How much is Camila’s investment worth after one year? $607.20 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 20 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #2 Felipe’s grandparents have given him $1500.00 to invest while he is in college to begin his retirement fund. He will earn 2.3% interest, compounded annually. What will his investment be worth at the end of four years? What is the equation? © Take Charge Today – June 2016 – Time Value of Money Math – Slide 21 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #2 Step One: Divide nr .023 1 .023 Step Three: Multiply by exponent 1.023 4 1.095 Step Two: Add 1 1 .023 1.023 Step Four: Multiply by principal 1.095 1500 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 22 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 1642.83 2.4.2.G1 Time Value of Money Math Practice #2 What will Felipe’s investment be worth at the end of four years? $1642.83 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 23 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #3 Nicole put $2000.00 into an account that pays 2% interest and compounds annually. She invests $2000.00 every year for five years. What will her investment be worth after five years? What is the equation? © Take Charge Today – June 2016 – Time Value of Money Math – Slide 24 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Time Value of Money Math Practice #3 Step One: Divide nr .02 1 .02 1 Step Three: Multiply by exponent 1.02 (1x5) Step Two: Add 1 1.104 2,000 1.02 Step Four: Subtract 1 1.104 Step Five: Multiply by principal 1.104 .02 208.16 1 .104 Step Six: Divide by rn 208.16 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 25 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona .02 2.4.2.G1 2.4.2.G1 Time Value of Money Math Practice #3 What will Nicole’s investment be worth at the end of five years? $10,408.08 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 26 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #4 Robert opens an account at a local bank. The account pays 2.4% interest compounded monthly. He deposits $100 every month for three years. How much is in the account after three years? What is the equation? © Take Charge Today – June 2016 – Time Value of Money Math – Slide 27 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Time Value of Money Math Practice #4 Step One: Divide nr .024 12 Step Two: Add 1 1 .002 100 1 1.075 1.075 Step Five: Multiply by principal .075 1.002 Step Four: Subtract 1 Step Three: Multiply by exponent (12x3) 1.002 .002 7.5 .075 Step Six: Divide by rn 7.5 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 28 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona .002 2.4.2.G1 2.4.2.G1 Time Value of Money Math Practice #4 What will Robert’s investment be worth at the end of three years? $3,750.00 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 29 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #5 When Daisy turned 15, her grandparents put $10,000 into an account that yielded 4% interest, compounded quarterly. When Daisy turns 18, her grandparents will give her the money to use toward her college education. How much will Daisy receive on her 18th birthday? What is the equation? © Take Charge Today – June 2016 – Time Value of Money Math – Slide 30 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #5 Step One: Divide nr .04 4 .01 Step Three: Multiply by exponent (4x3) 1.01 1.127 Step Two: Add 1 1 .01 1.01 Step Four: Multiply by principal 1.127 10,000 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 31 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 11,270 2.4.2.G1 Time Value of Money Math Practice #5 How much will Daisy receive on her 18th birthday? $11,270 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 32 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Practice calculating by entering all variables into the formula (advanced calculator) Use with Time Value of Money Math Practice – Advanced Calculator Worksheet Remember PEMDAS? When entering formulas into an advanced calculator, the order of operations matters. Use parenthesis to group your variables. © Take Charge Today – June 2016 – Time Value of Money Math – Slide 33 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #1 Camila deposited $600.00 into a savings account one year ago. She has been earning 1.2% in annual simple interest. Complete the following calculations to determine how much Camila’s money is now worth. Identify the variables P = 600 r = 1.2% =.012 t=1 On the calculator, you can save a step. By modifying the formula slightly, you can add the principal while making the interest calculation. FV = P(1+r)t Enter the whole formula at once: 600(1+.012)(1) © Take Charge Today – June 2016 – Time Value of Money Math – Slide 34 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #1 How much is Camila’s investment worth after one year? $607.20 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 35 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #2 Felipe’s grandparents have given him $1500.00 to invest while he is in college to begin his retirement fund. He will earn 2.3% interest, compounded annually. What will his investment be worth at the end of four years? Identify the variables: What is the equation? P = 1500 r = 2.3% =.023 n=1 t=4 Enter the whole formula at once: 1500(1+.023/1)^(1x4) © Take Charge Today – June 2016 – Time Value of Money Math – Slide 36 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #2 What will Felipe’s investment be worth at the end of four years? $1642.83 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 37 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #3 Nicole put $2000.00 into an account that pays 2% interest and compounds annually. She invests $2000.00 every year for five years. What will her investment be worth after five years? Identify the variables: What is the equation? P = 2000 r = 2% =.02 n=1 t=5 Enter the whole formula at once: 2000((1+.02/1)^(1x5)-1)/(.02/1) © Take Charge Today – June 2016 – Time Value of Money Math – Slide 38 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #3 What will Nicole’s investment be worth at the end of five years? $10,408.08 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 39 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Time Value of Money Math Practice #4 2.4.2.G1 Robert opens an account at a local bank. The account pays 2.4% interest compounded monthly. He deposits $100 every month for three years. How much is in the account after three years? Identify the variables: What is the equation? P = 100 r = 2.4% =.024 n = 12 t=3 Enter the whole formula at once: 100((1+.024/12)^(12x3)-1)/(.024/12) © Take Charge Today – June 2016 – Time Value of Money Math – Slide 40 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #4 What will Robert’s investment be worth at the end of three years? $3,728.90 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 41 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona Time Value of Money Math Practice #5 2.4.2.G1 When Daisy turned 15, her grandparents put $10,000 into an account that yielded 4% interest, compounded quarterly. When Daisy turns 18, her grandparents will give her the money to use toward her college education. How much will Daisy receive on her 18th birthday? Identify the variables: What is the equation? P = 10,000 r = 4% =.04 n=4 t=3 Enter the whole formula at once: 10000(1+.04/4)^(4x3) © Take Charge Today – June 2016 – Time Value of Money Math – Slide 42 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona 2.4.2.G1 Time Value of Money Math Practice #5 How much will Daisy receive on her 18th birthday? $11,268.25 © Take Charge Today – June 2016 – Time Value of Money Math – Slide 43 Funded by a grant from Take Charge America, Inc. to the Norton School of Family and Consumer Sciences at the University of Arizona