The Time Value of Money Future Value and Compounding

Now let's turn the rate of return formula (Formula 2.4) around to determine how money will grow over time given a rate of return.

Anecdote: Interest Rates over the Millennia

Historical interest rates are fascinating, perhaps because they look so similar to today's interest rates. Nowadays, typical interest rates range from 2% to 20% (depending on other factors). For over 2,500 years, from about the thirtieth century B.C.E. to the sixth century B.C.E., normal interest rates in Sumer and Babylonia hovered around 10-25% per annum, though 20% was the legal maximum. In ancient Greece, interest rates in the sixth century B.C.E. were about 16-18%, dropping steadily to about 8% by the turn of the millennium. Interest rates in ancient Egypt tended to be about 10-12%. In ancient Rome, interest rates started at about 8% in the fifth century B.C.E. but began to increase to about 12% by the third century A.C.E. (a time of great upheaval). When lending resumed in the late Middle Ages (twelfth century), personal loans in England fetched about 50% per annum, though they tended to hover between 10-20% in the rest of Europe. By the Renaissance, commercial loan rates had fallen to 5-15% in Italy, the Netherlands, and France. By the seventeenth century, even English interest rates had dropped to 6-10% in the first half, and even to 3-6% in the second half. Mortgage rates tended to be lower yet. Most of the American Revolution was financed with French and Dutch loans at interest rates of 4-5%.

Chapter 2


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