Time value of money
Why a dollar today is worth more than a dollar next year, and how finance puts a number on the difference. These lessons build compounding, discounting, level payments, bond prices and investment appraisal one at a time, each with a calculator you can change.
The real examples come from Apple's annual reports, which anyone can read on the US Securities and Exchange Commission website. Apple's net sales show compounding at work, its lease liability can be rebuilt by discounting, and its bonds show what rising interest rates do to a price. Every figure is tied out against the filing.
5 lessons, about 2 hours 13 minutes of reading in all. Start at the top and go in order.
After this module you will be able to
- grow a sum with compound interest and compare rates on an effective basis
- discount future amounts to present value and rebuild a reported liability
- price a loan or a stream of level payments, and see how interest and principal split
- price a bond and explain why its price moves against interest rates
- judge a project with net present value, internal rate of return and discounted payback
The lessons
- Compound InterestHow compound interest works: the formula, effective rates, real returns and the rule of 72, with a live calculator and Apple's net sales growth as an example.
- Present ValueWhat a future payment is worth today: the discounting formula, the choice of rate, and a rebuild of Apple's lease liability, with a live calculator.
- Annuities and LoansHow to price level payments: annuity formulas, loan payments and amortization, perpetuities, with a live loan calculator and Apple's lease liability.
- Bond Pricing and YieldHow a bond is priced from its coupon and yield, why prices fall when rates rise, and what Apple's debt note shows, with a live bond calculator.
- NPV, IRR and PaybackHow to judge a project with net present value, internal rate of return and payback, when they disagree, and Apple's lease as a borrowing rate. Live calculator.