1. Aim: Continuous Compounding Course: Math Literacy Aim: How does the exponential model fit into our lives? Do Now: An insurance agent wishes to sell you a policy that will pay you $100,000 in 30 years. What is the value of this policy in today’s dollars, if we assume a 9% annual inflation rate?

2. Aim: Continuous Compounding Course: Math Literacy y = a b x Where’d e Come From? Graph y  2.7183 y  2.7183 is asymptotic to f(x). Exponential function or e Leonard Euler

3. Aim: Continuous Compounding Course: Math Literacy The Power of e & Continuous Compounding y = a b x Exponential function Exponential growth in general terms y = P(1 + r) t Exponential growth Compound Interest Exponential growth Continuous compounding

4. Aim: Continuous Compounding Course: Math Literacy Exponential growth Compound Interest Exponential Function & Compounding y = a b x Exponential function Exponential growth in general terms y = P(1 + r) t e n  n   Exponential growth Continuous compounding Continuous growth/decay k is a constant (±)

5. Aim: Continuous Compounding Course: Math Literacy Application You invest $1050 at an annual interest rate of 5.5% compounded continuously. How much money, to the nearest dollar, will you have in the account after 5 years? P - principal or starting amount - 1050 r - annual interest rate – 5.5% t - time accruing interest – 5 years A - ending balance  $1382.36

6. Aim: Continuous Compounding Course: Math Literacy Application Find the amount in a continuously compounded account for the given conditions. Principal: $2000 Annual interest: 5.1% Time: 3 years Principal: $400 Annual interest: 7.6% Time: 1.5 years

7. Aim: Continuous Compounding Course: Math Literacy Application Compare the balance after 25 years of a $10,000 investment earning 6.75% interest compounded continuously to the same investment compounded semi-annually. Exponential growth Continuous compounding Exponential growth Compound Interest One earns $1484.49 more when compounded continuously

8. Aim: Continuous Compounding Course: Math Literacy Present Value How much money must you deposit in an account at 8.65% compounded continuously for 8 years and 135 days. = $109,276.64 Present Value Formulas

9. Aim: Continuous Compounding Course: Math Literacy Application On January 2, 2017, $4000 is placed in an Individual Retirement Account (IRA) that will pay interest of 4% per annum compounded continuously. a. What will the IRA be worth on January 1, 2057?