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Compound Interest Motivationβa choice between two investments (1) Pay $50,000 now for an expected profit of $100,000 after twelve years (2) Invest $50,000 at an interest rate of 7% for twelve years. Which option provides you with the most wealth in twelve years? Need to understand compound interest for an answer. 1 Option 2: Invest $50,000 at an interest rate of 7% for twelve years. Time now after 1 year Formula for wealth 50,000 50,000 + 50,000(0.07) =50,000(1.07) Wealth 50,000 $53,500 2 Option 2: Invest $50,000 at an interest rate of 7% for twelve years. Time now Formula for wealth 50,000 Wealth 50,000 after 1 year =50,000(1.07) $53,500 After 2 years ={50,000(1.07)}(1.0 $57,245 7) =50,000(1.07)2 3 Option 2: Invest $50,000 at an interest rate of 7% for twelve years. Time now after 1 year after 2 years after 3 years β¦ After 12 years Formula for wealth 50,000 =50,000(1.07) =50,000(1.07)2 =50,000(1.07)3 β¦ =50,000(1.07)12 Wealth 50,000.00 $53,500.00 $57,245.00 $61,252.15 β¦ $112,609.58 4 Which option makes us wealthier? (1) Pay $50,000 now for an expected profit of $100,000 after twelve years (2) Invest $50,000 at an interest rate of 7% for twelve years. Provides us with $112,609.58 in twelve years. Clearly this is the better option. 5 Terminology What is the future value of $50,000 invested at a 7% interest rate for twelve years? FV = (PV)(1+r)T FV = (50,000)(1.07)12 FV = $112,609.58 FV = future value PV = present value r = interest rate T = # years 6 More practice What is the future value of $100 invested at a 5% interest rate for 20 years? FV = (PV)(1+r)T FV = (100)(1.05)20 FV = $265.33 FV = future value PV = present value r = interest rate T = # years 7 Present value πΉπ = ππ 1 + π π πΉπ = ππ π 1+π πΉπ 1 + π βπ = ππ ππ = πΉπ 1 + π FV = future value PV = present value r = interest rate T = # years βπ 8 Present value How much money do we need to invest today at an interest rate of 5% to get $265.33 in 20 years? FV = future value PV = present value r = interest rate T = # years ππ = πΉπ 1 + π βπ ππ = 265.33 1.05 β20 ππ = $100 9 Present value How much money do we need to invest today at an interest rate of 3% to get $40,000 in 5 years? FV = future value PV = present value r = interest rate T = # years ππ = πΉπ 1 + π βπ ππ = 40,000 1.03 β5 ππ = $34,504.35 10 Back to the original question (1) Pay $50,000 now for an expected profit of $100,000 after twelve years. How much money do we need to invest today at 7% interest to receive $100,000 after 12 years? PV = (100,000)(1.07)-12 = $44,401.20 Clearly we prefer $50,000 dollars today over $44,401.20 dollars today. Itβs a bad investment. 11