1. A dollar today is worth more than a dollar tomorrow Calculating Simple Interest A dollar today is worth more than a dollar tomorrow Because of this cost, money earns interest over time If you are borrowing, you will pay interest If you are lending/investing, you will earn interest Simple Interest interest on an investment that is calculated once per period, usually annually on the amount of the capital alone interest that is not compounded

1. Calculating Simple Interest Principal is the initial amount invested or borrowed (the loan amount or how much you save) Simple Interest Formula: P = Principal r = Annual Interest Rate n = Number of periods (usually years) the money is being borrowed Simple Interest = Principal times interest times years Simple Interest = P(r)(n) Total Owed = P + P(r)(n)

1. Ex 1: Calculating Simple Interest Mr. Vasu invests $5,000. His annual interest rate is 4.5% and he invests his money for 5 years. What is the total in his account after this time? P = r = n = Total = P + P(r)(n) $5,000 0.045 5 5000 + 5000(0.045)(5) 5000 + 1125 = $6,125

1. Calculating Simple Interest Ex 2: Trayvond saves $10,000 to pay for a car. His earns 6% on his investment and invests his money for 7 years. What is the total in his account after this time? P = r = n = Total = P + P(r)(n) $10,000 0.06 7 10000 + 10000(0.06)(7) 10000 + 4200 = $14,200

2. Constant Multiplication Factor and Interest Rate Calculating Compound Interest Constant Multiplication Factor and Interest Rate The constant multiplication factor = (1 + r) r = annual interest rate (as a decimal) Annual interest rate and growth rate are the same thing Ex 1: If you earn 6%, what is the constant multiplication factor: (1 + 0.06) = (1.06) Ex 2: If the CMF is 1.5, what is the growth rate? 1.5 = 1 + r; r=0.50, which is 50%

2. Calculating Compound Interest Ex 3: Mr. Vasu invests $10,000 in an account that earns 6% annual interest that compounds annually. How much will he have in 2 years: Year 0 Year 1 Year 2 $10,000 10,000(1.06) = 10,600 10,600(1.06) = $11,236 Mr. Vasu has $11,236 after two years.

2. Calculating Compound Interest Ex 3: Mr. Vasu invests $10,000 in an account that earns 6% annual interest that compounds annually. How much will he have in 2 years: Year 0 Year 1 Year 2 $10,000 10,000(1.06) = 10,600 10,600 (1.06) = $11,236 =10,000(1.06)1 =10,600 10,000(1.06)(1.06) =10,000(1.06)2 =11,236 Ex 4: Mr. Vasu invests $10,000 in an account that earns 6% annual interest that compounds annually. How much will he have in 7 years? 10,000(1.06)7 = $15,036.30 Mr. Vasu has $15,036.30 after seven years.

2. Compound Interest Formula Calculating Compound Interest (Exponential Growth Function) A = P(1 + r)t A = Future Value or Final/Ending Value P = Principal/Initial Value and Y-Intercept r = Annual Interest Rate/Growth Rate t = Years

2. Ex 5: Aaliyah invests $6,000 and earns 5% per year. Calculating Compound Interest Ex 5: Aaliyah invests $6,000 and earns 5% per year. Write an exponential growth equation for how much money Aaliyah has after t years? A = ? P = 6,000 r = 0.05 t = ? A = 6000(1.05)t How much will she have after six years if interest is compounded annually? t = 6 years A = 6000(1.05)6 A = $8,040.57

2. Ex 6: Ganiu invests $24,000 for ten years at 4.5%. Calculating Compound Interest Ex 6: Ganiu invests $24,000 for ten years at 4.5%. How much does he have in his account after the ten years? A = ? P = 24,000 r = 0.045 t = 10 A = 24000(1.045)10 A = $37,271.27 Ganiu has $37,271.27 after 10 years. How much did he earn in interest alone? $37,271.27 – 24,000 = Ganiu earned $13,271.27 in interest.

3. Analyzing Compound Interest Formula Ex 7: The following function represents how much money Lashawn has in her account after t years: A(t) = 6,500(1.17)t What is the y-intercept? A(t) = b(a)x The y-intercept is 6,500. What is the constant multiplication factor? A(t) = b(a)x The CMF is 1.17. How much money does Lashawn invest at the beginning into her account? The y-intercept is where t=0, the initial value. So, she started with $6,500. What is the annual interest rate? CMF = (1+r) = 1.17, so r = 0.17 or 17% How much Lashawn have after twelve years? A(t) = 6,500(1.17)12 = $42,770.44.

3. Analyzing Compound Interest Formula Ex 8: The following function represents the number Chinese people living the city of Kunming: C(t) = 50,000(2)t What is the y-intercept? A(t) = b(a)x The y-intercept is 50,000. What is the constant multiplication factor? A(t) = b(a)x The CMF is 2. How many people were initially in Kunming? The y-intercept is where t=0, the initial value. So, the initial population was 50,000 people. What is the annual growth rate in population? CMF = (1+r) = 2, so r = 1 or 100% growth How many people in Kunming after 10 years? C(t) = 50,000(2)10 = 51,200,000 people

4. A = P(1 + r/n)nt Compound Interest Formula Calculating Compound Interest w Periodic Compounding Semiannual Quarterly Monthly Daily Compound Interest Formula with Periodic Compounding A = P(1 + r/n)nt A = Future Value or Final/Ending Value : P = Principal/Initial Value and Y-Intercept r = Annual Interest Rate/Growth Rate t = Years n = Periods per Year (1, 2, 4, 12, 365)

4. Calculating Compound Interest w Periodic Compounding Semiannual Quarterly Monthly Daily Ex 9: Devin invests $6,000 and earns 5% per year. How much will he have after six years A(t) = 6000(1 + .05/n)(n●6) if interest is compounded annually (n=1)? A = 6000(1.05/1) (1●6) A = 6000(1.05) 6 A = $8,040.57 if interest is compounded semi-annually (n=2)? A = 6000(1 + 0.05/2)(2●6) A = 6000(1.025)12 A = $8,069.33 if interest is compounded quarterly (n=4)? A = 6000(1 + 0.05/4)(4●6) A = 6000(1.0125)24 A = $8,084.11

4. Calculating Compound Interest w Periodic Compounding Semiannual Quarterly Monthly Daily Ex 9: Devin invests $6,000 and earns 5% per year. How much will he have after six years A(t) = 6000(1 + .05/n)6n if interest is compounded monthly (n=12)? A = 6000(1 + 0.05/12)(12*6) A = $8,094.11 if interest is compounded daily (n=365)? A = 6000(1 + 0.05/365)(365●6) A = $8,098.99 Devin’s investment gets bigger if interest compounds more frequently Annually Semi-Annually Quarterly Monthly Daily n = 1 n = 2 n = 4 n = 12 n = 365 $8,040.57 $8,069.33 $8,084.11 $8,094.11 $8,098.99

5. Simple vs. Compound Interest Linear vs. Exponential Functions Ex 10: Homer invests $1,000 at 10% for nine years P = 1,000 r = 0.10 t = 9 Simple Interest Compound Interest (annual) Asimple = P + Prt A = 1000 + 1000(0.10)(9) Asimple = $1,900 Acompound = P(1+r)t A = 1000(1.10)9 Acompound = $2,357.95 Year A(t) 1,000 1 1,100 2 1,200 3 1,300 4 1,400 5 1,500 9 1,900 Year A(t) 1,000 1000(1.1)0 1 1,100 1000(1.1)1 2 1,210 1000(1.1)2 3 1,331 1000(1.1)3 4 1,464 1000(1.1)4 5 1,611 1000(1.1)5 9 2,358 1000(1.1)6