Cheat sheet

Money over time: cheat sheet

The summary, key terms and the trap to avoid for every lesson, in order. Print it, or read it, cover it, and say it back.

Compound interest Mankiw ch. 14

Compounding: interest earns interest.
Future value = amount × (1 + r)ᴺ, with r as a decimal.
Simple interest only ever uses the original amount.
Rule of 70: doubling time ≈ 70 ÷ rate.
Small rate differences become large over long periods.

future value: what an amount grows to after interest
compounding: earning interest on earlier interest
simple interest: interest on the original amount only
rule of 70: doubling time ≈ 70 ÷ growth rate (%)

Watch out: Multiplying the rate by the number of years. "6% for 10 years is 60%" is simple interest. Compounding gives about 79% here, and the gap grows every year.

Present value Mankiw ch. 14

Money today is worth more than the same money later.
Present value = future amount ÷ (1 + r)ᴺ.
Higher interest rates mean lower present values.
Compare offers paid at different times by their present values.

present value: what a future amount is worth today
discounting: working out a present value
interest rate: the price of waiting; higher rates shrink present values

Watch out: Adding up future payments as if they were all paid today. A prize of 10,000 a year for 30 years is "300,000" on paper, but each later payment is worth less today, so its present value is well below 300,000.

Measuring inflation with a price index Mankiw ch. 11

Inflation is a rise in the general level of prices.
A price index tracks the cost of a basket over time; the basket is held fixed between updates.
Index = cost now ÷ cost in base year × 100.
Inflation is the percentage change between two index values.

consumer price index (CPI): cost of a basket of goods, held fixed between updates, compared with a base year
base year: the year the index is set to 100
inflation rate: percentage change in the price index from one period to the next

Watch out: Reading the index level as the inflation rate. An index of 106.25 does not mean prices rose 106%. It means prices are 6.25% above the base year. Inflation is always the change between two index numbers.

Real and nominal interest rates Mankiw ch. 11

Nominal: how fast the money grows. Real: how fast what it buys grows.
Real ≈ nominal − inflation.
If inflation beats your interest rate, you can buy less.
With deflation, the real rate is above the nominal rate.

nominal interest rate: the rate you are quoted, not corrected for inflation
real interest rate: the rate corrected for inflation: about nominal − inflation
purchasing power: how much your money can buy
deflation: falling prices

Watch out: Thinking you are richer because the balance went up. If inflation is higher than your interest rate, the balance rises while what it buys shrinks.

Investors as a group earn the market minus costs Costs and the market

Before costs, investors as a group earn the market return; trading among them moves money around but adds nothing.
After costs, the group must earn less, by exactly what it pays to brokers, managers, advisers and the tax collector.
Costs come every year and compound, like interest in reverse.
Judge a cost by what it takes over the whole time you hold something.

market return: the return of the whole market
zero-sum: one side's gain is another side's loss
index fund: a fund that simply holds all the shares in a market (or an index), in proportion, and keeps them
expense ratio: a fund's yearly running costs, as a % of what you hold
commission: a fee paid to a broker for each trade
Helpers: Bogle's name for brokers, managers and advisers paid by investors

Watch out: Thinking that because some investors beat others, investors as a group can beat the market. Every gain from a trade is another investor's loss. Only the Helpers are sure to come out ahead.