Modified duration is a formula that measures the value of a bond in relation to changes in interest rates. Modified duration determines how a bond's price will change, in percentage terms, relative to a fall or rise in interest rates by a percentage point.

The modified duration is calculated by dividing the value of the Macaulay duration by 1 plus the yield to maturity, divided by the number of coupon periods per year. The modified duration formula determines how much the duration changes for each percentage change in yield. The modified duration also determines how a 1% change in interest rates will affect a bond's price. The yield to maturity calculates a bond's return and takes into account the bond's current price, par value, coupon interest rate and the time to maturity. Since a bond's price and interest rates are inversely related, there is an inverse relationship between modified duration and yield to maturity.

Modified duration is an adjusted version of the Macaulay duration, which accounts for changing interest rates. The Macaulay duration needs to be calculated before calculating the modified duration. The Macaulay duration is calculated by adding up, over the total number of periods, the time frame multiplied by the coupon payment per period divided by 1, plus the yield per period raised to the time periods. This value is added to the total number of periods multiplied by the maturity value divided by 1 plus the yield per period raised to the total number of periods. Then the value is divided by the current bond price. In simple terms, the Macaulay duration formula is the present value of a bond's cash flows multiplied by the length of the time periods and divided by the bond's current market price.

A bond's price is calculated by multiplying the cash flow by 1 minus 1 divided by 1 plus the required yield raised to the number of cash flows divided by the required yield. This value is added to the par value of the bond divided by 1 plus the required yield raised to the number of cash flows.