Question

A bond that pays interest annually yields a rate of return of 8.75 percent. The inflation rate for the same period is 3 percent. What is the real rate of return on this bond?

Answer 1

To calculate the real rate of return, you can use the Fisher equation, which relates nominal interest rates, real interest rates, and inflation rates. The formula is:

\[
1 + r = \frac{1 + i}{1 + \pi}
\]

Where:
- \( r \) is the real rate of return,
- \( i \) is the nominal rate of return (the bond's yield), and
- \( \pi \) is the inflation rate.

In your case:
- \( i = 0.0875 \) (8.75 percent as a decimal)
- \( \pi = 0.03 \) (3 percent as a decimal)

Now, plug the values into the equation:

\[
1 + r = \frac{1 + 0.0875}{1 + 0.03}
\]

Calculating the values:

\[
1 + r = \frac{1.0875}{1.03}
\]

\[
1 + r = 1.0565
\]

Now, to find \( r \):

\[
r = 1.0565 - 1 = 0.0565
\]

To convert it back to a percentage:

\[
r = 0.0565 \times 100 = 5.65\%
\]

Thus, the **real rate of return on the bond** is approximately **5.65%**.