Compound Interest and Inflation

Introduction

Compound interest means you earn interest on your original money and on the interest already earned. Over long periods this creates big differences. Inflation works in the opposite direction: it reduces what your money can buy. Understanding both helps with saving and borrowing. The figures here are illustrations, not predictions.

The compound formula

For a one-time deposit:

future value = principal x (1 + rate) ^ years

Example: 1,000 at 4 percent a year for 5 years.

1,000 x 1.04 ^ 5 = 1,216.65

The simple-interest total would be 1,000 + 5 x 40 = 1,200. The extra 16.65 is interest earned on interest. Over longer periods the gap widens quickly. At 5 percent for 10 years, 1,000 becomes 1,628.89.

Regular saving

Saving 200 a month for 10 years at an assumed 5 percent a year, compounded monthly, grows to about 31,056. Your own contributions are 200 x 120 = 24,000, so about 7,056 is growth. The longer the time, the larger the share from growth.

Time matters more than most people expect. The earlier you start, the longer compounding works. But returns are never guaranteed. Savings accounts pay low, steady rates, while investments can rise and fall, as later lessons explain.

The rule of 72

A rough shortcut: years to double is about 72 divided by the annual rate in percent. At 5 percent, 72 divided by 5 is 14.4 years. The exact answer is about 14.2 years. The rule is an approximation that works best for rates around 6 to 10 percent.

Compound interest works against borrowers

Debt compounds too. A card balance at a high rate can grow quickly if unpaid. The same maths that helps savers hurts borrowers.

Inflation

Inflation is the general rise in prices over time. If inflation is 3 percent a year, something costing 100 now costs about 103 next year. Equivalent: your money buys less.

At 3 percent for 10 years, 100 of today's money has the buying power of about 74.41 in today's terms (100 divided by 1.03 to the power 10). Over 30 years the loss is larger.

Real versus nominal returns

• Nominal return: the stated rate, such as 4 percent.
• Real return: the return after inflation. An approximation is nominal minus inflation. More exactly, (1 + nominal) divided by (1 + inflation) minus 1.

If savings pay 4 percent and inflation is 3 percent, the real return is about 0.97 percent. If inflation is higher than your interest rate, the real return is negative, and your money loses buying power while its number grows.

Fees also compound

A small yearly fee reduces growth every year. For example, 1,000 growing 7 percent a year for 30 years reaches about 7,612. At 6 percent after a 1 percent yearly charge, it reaches about 5,743. The 1 percent difference costs about 1,869, roughly a quarter of the potential result. Always check fees.

Try it yourself

Use a spreadsheet to calculate 1,000 at 3, 5 and 7 percent for 10, 20 and 30 years. Then calculate what 1,000 today could buy in 20 years at 2, 3 and 5 percent inflation.

Summary

• Compound interest earns interest on interest, and time makes a large difference.
• Inflation reduces buying power, so real returns matter more than nominal ones.
• Fees and high-interest debt compound too, so check costs carefully.