Finance & Investment Math

Compound Interest: Why Money Grows the Way It Does

Put an amount P to work at an annual rate r, and after n years you have A. What makes compound interest different is that the interest earns interest too — and the gap between that and simple interest widens dramatically the longer you leave it alone. Tax-advantaged retirement accounts exist for exactly this reason: keep the tax off the gains and the compounding runs at full strength.

Present Value and the Discount Rate

Money you get later is worth less than money you have now — inflation eats into it, and you gave up whatever else you could have done with it in the meantime. To find what a future amount FV, arriving n years from now, is worth today, you discount it at rate r. Every investment decision, every company valuation, every comparison between two loan offers comes back to this one idea.

Expected Return: The Average Outcome of an Investment

Sketch out a few scenarios — a strong economy, a normal one, a downturn — give each a probability and a return, and the weighted average is your expected return. It's the starting point for any estimate of what a stock might do. On its own it says nothing about how bumpy the ride is; pair it with the standard deviation and you can compare investments on a risk-adjusted basis.

The Rule of 72: Compound Interest in Your Head

A shortcut for how long money takes to double. At 3% a year, 72 ÷ 3 = 24 years. At 6%, 72 ÷ 6 = 12 years. It isn't exact, but it's close enough and fast enough that you can sanity-check a salesperson's projection while they're still talking.