 Time Value of Money Time Value of Money Warm-Up Directions: Select the most appropriate answer for each question. 1. Which would you rather have? \$100 today \$100 one year from today 2. If the interest rate is 5%, \$100 today is basically equal to ___ one year from now.

\$95 \$100 \$105 \$150 1. If you lent a friend \$50 two years ago and the interest rate is 2%, he or she now owes you approximately

\$48 \$100 \$50 \$52 2. Which of these is the most valuable, if the interest rate is 10%?

Time Value of Money \$800 today \$1000 three years from now \$2000 ten years from now \$3000 twenty years from now Warm-Up Answers Directions: Select the most appropriate answer for each question. 1. Which would you rather have? \$100 today

\$100 one year from today 2. If the interest rate is 5%, \$100 today is basically equal to ___ one year from now. \$95 \$100 \$105

\$150 1. If you lent a friend \$50 two years ago and the interest rate is 2%, he or she now owes you approximately \$48 \$100 \$50 \$52

2. Which of these is the most valuable, if the interest rate is 10%? Time Value of Money \$800 today \$1000 three years from now \$2000 ten years from now \$3000 twenty years from

now What is your money worth? Would you rather have \$100 today or \$100 one year from today? Time Value of Money #1 Inflation: Money loses value In 2000, \$100 buys 40 Big Macs (\$2.50 each) In 2018, \$100 buys 28 Big Macs (\$3.57 each) Time Value of Money

#2 Interest: Money grows over time \$100 invested in an S&P indexed stock fund in 2000 would be worth approximately \$338 today \$100 today is worth \$100 today Time Value of Money If I want the most money... Should I pay off my house now, or invest cash in a stock account? Should I overpay my income tax during the year, to get a refund? Or underpay and owe money at tax time? How much should I pay to take over someones business?

Time Value of Money Wheres that money you owe me? Time Value of Money The Calculation Invest \$100 for 1 year at 5% interest: \$100 + (0.05) x \$100 = \$105 Time Value of Money The Calculation You can use algebra to rearrange this equation:

\$100 + (0.05) x \$100 = \$105 \$100 x (1 + 0.05) = \$105 You can also change \$100 to X (to represent any amount you would invest) and 5% to r (to represent any interest rate) X x (1 + r) = future value Time Value of Money The Calculation It gets a little more complicated when we include compound interest (meaning your interest earns interest) AND include multiple years. The # of years or periods is an exponent, which allows you to earn interest every year or multiple times a year.

X (1 + r)#periods = future value x Time Value of Money The Calculation Lets consider Jerrys situation. Leo owes his mom \$50 for 53 years. Jerrys dad is compounding the interest quarterly 4 times a year at 5%. X (1 + r)#periods = future value x \$50 (1 + .05/4)212 = future value

x Time Value of Money Online Calculator https://www.investopedia.com/calculator/fvcal.aspx Time Value of Money The Calculation How to calculate future value: X (1 + r)#periods = future value x

How to calculate present value: value X = future (1 + r)#periods Time Value of Money Online Calculator Calculate future value of a present dollar amount: https://www.investopedia.com/calculator/fvcal.aspx Calculate present value of a future dollar amount: https://www.investopedia.com/calculator/pvcal.aspx Time Value of Money

Which has the highest present value? Assume an interest rate of 10%, interest calculated annually a. b. c. d. \$800 today \$1000 3 years from now \$2000 10 years from now \$3000 20 years from now

Present Value calculator: https://www.investopedia.com/calculator/pvcal.aspx Time Value of Money