1. 3.1 (part 2) Compound Interest & e Functions I.. Compound Interest: A = P ( 1 + r / n ) nt A = Account balance after time has passed. P = Principal: $ you put in the bank. r = interest rate (written as a decimal). n = number of times a year the interest is compounded. (annual = 1, semi-annual = 2, quarterly = 4, monthly = 12, etc.) t = time (in years) the money is in the bank. A) To determine the Account balance after time has passed, plug all the #s into the formula and simplify.

2. 3.1 (part 2) Compound Interest & e Functions Example: 1) If you deposit $4000 in an account that pays 2.92% interest semi-annually, what is the balance after 5 years? How much did the account earn in interest? A = P ( 1 + r / n ) nt  A = 4000 ( 1 +.0292 / 2 ) 25 A = 4000 ( 1 +.0146 ) 10 A = 4000 (1.0146) 10 A = $ 4623.90 So the account gained $623.90 dollars in the 5 years.

3. 3.1 (part 2) Compound Interest & e Functions Example: 2) If you deposit $12,500 in an account that pays 4.5% interest quarterly, what is the balance after 8 years? How much did the account earn in interest? A = P ( 1 + r / n ) nt  A = 12500 ( 1 +.045 / 4 ) 48 A = 12500 ( 1 +.01125 ) 32 A = 12500 (1.01125) 32 A = $ 17,880.64 So the account gained $5380.64 dollars in the 8 years.

4. 3.1 (part 2) Compound Interest & e Functions II.. The Natural Base e. A) e ≈ 2.72 B) “e” occurs in nature and in math/science formulas. C) definition: e = as “n” approaches + ∞. D) y = ae bx+c + d is the natural base exponential function. E) y = e bx is the parent function: critical pt at (0, 1) 1) + b = Growth graph 2) – b = Decay graph 3) Horizontal asymptote: y = 0.

5. 3.1 (part 2) Compound Interest & e Functions III.. Continuously Compounded Interest: A = Pe rt A) Convert the interest rate to a decimal. 1) Move the decimal two places to the left Example: 3) Find the account balance after you invest $5,000 in a 3.5% continuously compounding account for 8 years. A = 5000 e^(.0358) A = $ 6615.649062 Round money off to the nearest penny (2 decimal places). A = $ 6615.65

6. 3.1 (part 2) Compound Interest & e Functions IV. Solving Exponential Equations (that have common bases). A) Break down both sides of the = sign into the same base #. 1) Break all bases down into a common base. a) Remember that 2) Exponent property: (3 4 ) x+2 = 3^(4x + 8) 3) Set “ exponent = exponent” by crossing off the bases. a) base expo = base expo (gives expo = expo) 4) Solve for the variable. Homework page 227 # 33 – 40 all, 45 – 54 all