Foundations of Finance

01Defining Finance and the Financial System 02Valuation and Management: The Two Challenges 03Stocks, Flows, and the Five Cash-Flow Decisions 04Time, Risk, and the Six Principles of Finance 05How to Learn Finance: Practice and Study Habits Problem set0/10 Problem set 20/10 Practice∞

Present Value

01Information and Price: An Auction and Fannie Mae 02Who Pays for the Fannie and Freddie Guarantee?03What Counts as an Asset: Patents, Secrets, Brands 04An Asset as a Sequence of Dated Cashflows 05The Value Operator and the Cashflow Timeline 06Dates as Currencies: Building Net Present Value 07Discount Factors: Market Prices for Future Dollars 08A Worked Net Present Value and Its Assumptions 09The Opportunity Cost of Capital and Present Value Problem set0/10 Problem set 20/10 MIT problem set0/5 Practice∞

01Does the Currency Change an NPV's Sign?02Moral Hazard and Contagion: Where Bailouts Stop 03The NPV Rule at Work, and Choosing the Rate 04The Perpetuity: Why Cash Forever Is Worth C/r 05Reading the Rate Off a Perpetuity's Price 06The Growing Perpetuity, and When Growth Outruns r 07Building the Annuity from Two Perpetuities 08The Annuity Discount Factor and Mortgage Payments 09APR, the Effective Annual Rate, and Compounding Problem set0/10 Problem set 20/10 MIT problem set0/13 Practice∞

APR, the Effective Annual Rate, and Compounding

What could a depositor do to beat a posted annual rate, and which convention do banks use to stop them?

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Your summary note

1. Pro-rating a quoted rate and redepositing
  Work through half of ten percent paid after six months followed by an immediate redeposit, and write the rate $\sqrt{1.10} - 1 \approx 4.881\%$ that leaves the year at exactly ten percent.
2. The effective annual rate $\left(1 + \frac{r}{n}\right)^n - 1$
  Define the annual percentage rate and the number of compounding periods, then tabulate $1,000 at ten percent compounded annually, semiannually, quarterly and monthly, and record the depositor and borrower sides.
3. Disclosure of the APR and the annual percentage yield
  Record the Truth in Lending requirement on loans and the Truth in Savings requirement on deposits, and note that a stated APR is incomplete without its compounding frequency.
4. Continuous compounding as $n \to \infty$
  Take the limit of the effective annual rate as compounding grows unbounded, write $r_{\text{EAR}} = e^{r} - 1$ , and evaluate it at a ten percent annual percentage rate.
Attempt 1 of 2