Unpacked Content
Knowledge
Students know:
- how to select information from a real-world financial problem, such as the initial amount of the investment and its periodic rate of change, and use it along with a geometric sequence to model compound interest and proportional depreciation.
Skills
Students are able to:
- Identify the first term and common ratio in a geometric sequence.
- Recognize that the first term of a geometric sequence is the initial value of the loan or investment.
- Recognize that the common ratio is either (1+rate of growth) or (1-Rate of decay).
- Use a geometric sequence to model compound interest or proportional depreciation.
- Display data found using a geometric sequence to model compound interest or proportional depreciation. Relate APR to APY using compound interest formulas.
Understanding
Students understand that:
- the initial amount of an investment or a loan and its periodic rate of change correlate to the first term and the common difference in a geometric sequence.
- Geometric sequences can be used to model compound interest and proportional depreciation.
- The annual percentage rate is the yearly rate of interest while the annual percentage yield is the rate you actually pay when compound interest is included.
Vocabulary
- Compound Interest
- Geometric Sequence
- Proportional Depreciation
- Periodic
- Annual Percentage Rate
- Annual Percentage Yield
