How to Calculate Modified Duration

By Motley Fool Staff – Updated Apr 29, 2025 at 10:58 PM EST

Key Points

Modified duration shows bond price sensitivity to yield changes; a 1.859% price change per 1% yield shift.
Macauley duration measures average time to receive bond cash flows, key for calculating modified duration.
High modified duration increases a bond's interest rate risk, crucial in rising-rate environments.

In many ways, bonds are more complex than stocks. Investors use a host of different metrics to evaluate bond investments, and one involves a concept known as duration, which helps an investor understand how sensitive a bond's value is to interest rate changes. There are several different types of duration calculations, but one involves what's known as modified duration and produces the percentage change in price for a given change in interest rates.

Loading paragraph...

Person sits at window while working on laptop, paperwork and phone. — Image source: Getty Images.

Loading image...

Loading paragraph...

Loading pitch...

For example, say you have a two-year bond paying annual interest at 5% and with a yield to maturity of 5%. Its current price is $1,000. The present value of the first payment would be (1000 x 5%) / (1 + 5%), or $47.62. The present value of the second payment, including the maturity amount, would be ((1000 + (1000 * 5%) / (1 + 5%)^2), or $952.38. So the Macauley duration would be (($47.62 x 1) + ($952.38 x 2)) / ($47.62 + $952.38), which works out to 1.952.

To calculate modified duration, you take the answer above and divide it by the sum of 1 and the bond's yield to maturity. So 1.952 / (1 + 5%) = 1.859.