Mathematical Preliminaries – Working with Interest Rates
Bibliographic record
Abstract
Learning Objectives In this chapter, we will review the concepts of interest rates and time value of money (TVM). There are several types of present-value and future-value formulas, each of which is used in specific circumstances. Our goal is to make sure that you understand when (i.e., in what context) these formulas should be used. A good understanding of this chapter is needed to proceed to future chapters, where we will need to calculate the amounts of your consumption and savings at various points in time. Although we believe that most of you have covered these materials in your previous finance courses, we recommend that you take another look at them and familiarize yourself with the notations we will use in the rest of this book. Interest Rates As you may recall, an interest rate is the rate of return that a borrower promises to pay for the use of money that he or she borrows from the lender. Normally, it is expressed in terms of per-annum percentage rates (e.g., 4% p.a.). To express it properly, however, we also need to state the compounding frequency of the rate, which is the number of compounding periods in one year. In other words, it is the number of times in a year that interest is calculated and added to the principal of the loan. For example, annual compounding means that interest is added to the principal once a year. Suppose you invest $1 for one year at the interest rate of 4% p.a., annual compounding.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.022 | 0.021 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".