 S = future worth  P = principal  r = annual rate  t = time in years  m = number of compoundings per year Compound Interest and Sequences if compounded.

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Presentation transcript:

 S = future worth  P = principal  r = annual rate  t = time in years  m = number of compoundings per year Compound Interest and Sequences if compounded continuously. When compounded more than once a year, the effective annual rate (or annual percentage yield) is:

What would a $5000 investment be worth in 3 years if the interest rate is 7.5% and the investment is compounded: yearly semiannually monthly continuously n S Example Effective annual rate for the monthly investment:

Fill in the table

Consider the following sequences: Geometric Sequences A geometric sequence is defined as: 3, 6, 12, 24, 48, … 81, 27, 9, 3, 1, … with a as the first term and r as the common ratio.

Examples Find the common ratio, the nth term, and the 20 th term.

Partial Sums The partial sum of a geometric sequence looks like:

Example Find the 20 th partial sum for geometric sequence with a = 5, r = 2:

Preview of Annuities Make yearly payments of $200 to an account that has an annual interest rate of 5%. What is the account worth after the 10 th payment is made?