Time Value of Money The time value of money is the idea that money available now is worth more than the same amount in the future - this is essentially why interest exists. Present value is the current value of a sum that you are expecting to be paid in the future Ex: How much a bond, which can be cashed out in 2 years, is worth today Future value is the value of an asset or cash at a specified date in the future, based on its value now, and interest Ex: How much $100 will be in 2 years, if earning 5% interest Grab a whiteboard- let s practice!
Future Value Review: How much will a current interest-earning investment be worth in the future? Sally can put $1000 into a CD earning 4% compounded interest for 5 years What is the future value of her investment? Show your work!
Future Value Review: How much will a current interest-earning investment be worth in the future? Sally can put $1000 into a CD earning 4% compounded interest for 5 years What is the future value of her investment? $1000(1 +.04) 5 = $1216.65
Future Value Review: How much will a current interest-earning investment be worth in the future? Rupert buys a $500 bond earning 2% compounded interest for 20 years What is the future value of his investment? Show your work!
Future Value Review: How much will a current interest-earning investment be worth in the future? Rupert buys a $500 bond earning 2% compounded interest for 20 years What is the future value of his investment? $500(1 +.02) 20 = $742.97
Present Value vs Future Value Scenario: You win $1 million in the lottery. Choices: Get the whole $1 million in two years, OR a smaller sum right now. Which do you choose? In order to make an informed decision, we would need to determine the present and future values.
Money Now or Later? It depends on the present and future value of the money. We know the future value: $1 million (in 2 years) However, what is the minimum amount we would be willing to accept right now? Need to know the interest rate! Let s say that the expected interest rate is 5% and officials are offering you $910,000 now. Do we take the offer?
Formulas PV = present value R = interest rate FV = future value n = number of years Future Value Formula FV = PV(1 + r) n Present Value Formula PV = FV/(1 + r) n Now calculate the present value of the $1 million dollar deal on your whiteboard. Should we take the deal?
Yes take the deal! PV = 1,000,000/(1+.05) 2 PV = $907,029.47 Money Now or Later? Present values is less than what they are offering, $910,000. So, take the deal! Another way to look at it: If we take the $910,000 now and invest it at 5% interest for two years, we will have more than $1 million dollars. $910,000(1+.05) 2 = $1,003,275.00
Let s Practice! #1. The Federal Reserve issues a $1,000, one year T-Bill (Treasury Bill) paying 5%. The buyer receives the $1,000 at the date of maturity, which is 1 year from now. You pay the present value of the T-Bill upon purchase. What is your purchase price? Show your work!
Let s Practice! #1. PV = 1000/(1 +.05) 1 PV = $952.38
Let s Practice! #2. Suppose you want to get a lump sum payment of $100,000 two years from now. If the current interest rate is 10%, how much will you need to invest now, in order to meet your goal? In other words, what is the present value of $100,000 two years from now? Show your work!
Let s Practice! #2. PV = $100,000(1 +.10) 2 PV = $82644.63
#3. You lend this jabroni $500, and he promises to pay you back in 2 years. You agree to have him pay you back with a compound interest rate of 3% at the end of two years. How much does he owe you in two years? Let s Practice!
Let s Practice! #3. FV = $500(1 +.03) 2 FV = $530.45
Let s Practice! #4. You are planning to move out of your parents house in 3 years and want to start saving now for your first month s rent and deposit. You ve calculated that you ll need $3,000. How much money would you need to save now, if you can get an interest rate of 2%, in order to have the money for your new place?
Let s Practice! #4. PV = $3000/(1 +.02) 3 PV = $2826.99