2 6 Continuous Compounding Advanced Financial Algebra How

2 -6 Continuous Compounding Advanced Financial Algebra

How can interest be compounded continuously? Compound interest means that you are paid interest on your balance AND on previous interest you have earned. Compound interest allows your money to grow FASTER and we have compounded annually (once a year), quarterly (4 times per year), monthly (12 times per year), daily (365 times per year), etc. With computers, we can compound interest every second or microsecond or faster which becomes continuously.

Developing formula

Example 1 – as x increases, what happens to y? Given the quadratic function f(x) = x 2 + 3 x + 5 and the linear function g(x) = 5 x + 1, as the values of x increase to infinity, what happens to the values of y? SOLUTION: Look at the graphs to the right. F(x) is pink and g(x) is yellow. For f(x), as the x values increase to the right, the y values also increase. For g(x), as the x values increase to the right, the y values decrease.

Example 2 – hyperbola limit

Example 3 – evaluate the limit using graph x y or f(x) 0 1 2 3 4 5

Continuous Compounding Formula

Example 6 – another scenario

Assignment: pg 107 #2 b-i only, #4, 5, 7 #2

Assignment: pg 107 #2 b-i only, #4, 5, 7 cont. #4 #5 #7