# Bonds, interest rates and inflation

I was reading Learn to Earn by Peter Lynch and I came across a paragraph that has confused me to say the least. It is regarding bonds -

If you buy a \$10,000 ten-year bond and hold it for ten years, you get your money back plus interest, and nothing more. Actually, you get back much less because of inflation. Let’s say the bond is paying 8 percent a year, and the inflation rate over that ten-year period is 4 percent. Even though you’ve collected \$8,000 in interest payments, you’ve lost almost \$1,300 to inflation. Your original \$10,000 investment is now worth \$6,648 after ten years of 4 percent annual inflation. So the whole ten-year investment has left you with less than a 3 percent annual return, and that’s before taxes. If you figure in the taxes, your return approaches zero.

I can calculate the interest payment as \$8,000. I can also see how the investment of \$10,000 is now worth only \$6,648 after ten years of 4 percent annual inflation.

But my question is, how do we arrive at "lost almost \$1,300" part? Would be great if you could explain.

• I'd assume he means that you've lost \$1,300 of your \$8,000 in interest to inflation (\$800 each year eroded by 4%), but I get ~\$1,565 not \$1,300, so it's unclear to me. – Hart CO Apr 23 at 16:05
• @HartCO Could you tell me how you arrived at ~\$1,565? At 4% annual inflation, the \$8,000 interest comes to be \$5,318. That gives me a loss of \$2,682 – Kumaravel Rajan Apr 23 at 16:09
• Without getting in to the relative merits of being concerned with the inflation boogy-man, logically, shouldn't the risk free investment option have a net-net return of close to zero? You're being paid a nominal amount for your loss of liquidity. You never assumed any real investment risk why would anyone expect real investment reward? – quid Apr 23 at 17:18
• I'm not sure what the point of mentioning inflation is. Inflation affects all investments, so I don't know why he's only applying it to bonds. – D Stanley Apr 23 at 18:05
• After reading that paragraph about 10 times I would argue that you should pick something else to read. – xyious Apr 23 at 19:37

This passage seems designed to confuse rather than teach. However:

Amount of principle lost to inflation: 10000*.96^10 = \$6648

Amount of interest lost to inflation (compounded yearly and assuming you don't reinvest): 800*.96^9+800*.96^8+800*.96^7+800*.96^6+800*.96^5+800*.96^4+800*.96^3+800*.96^2+800*.96^1+800 = \$6703

The second number seems to be the "lost almost \$1,300" (of the \$8000 interest).

It appears that Mr. Lynch made liberal use of first-order approximations to elaborate his point.

According to his math:

``````\$6,648 present value of bond = \$10,000 face value * (1-0.04 inflation)^10
"Lost to inflation" = present value - face value ≅ -\$1300

# (I'm guessing a bit on this next one)
"less than a 3 percent annual return"
= ((1+(interest rate * 10))/(1+(inflation rate * 10)))-1 / 10
= (1.8/1.4)-1 / 10
= 0.0286
``````

These are arithmetic approximations of what should be a geometric calculation. I don't believe this is a contentious topic. Please look at an explanation of inflation discounting or Google another one if you prefer.

If you want to know what the rate of return on an investment is after inflation:

``````real rate = (1 + interest rate)/(1 + inflation rate) - 1
= 1.08 / 1.04 -1
= 0.038
``````