Duration$$gap$=$Asset$$Duration$$Liability$$Duration$$LiabilityAsset

where Asset$$is the market value of the asset, Liability$$is the market value of the liability, and duration$$is the weighted average of times until payment, with their weights proportionate to the present value of the payment: Duration$=$t$=1$n$($t$$Paymentt$(1+$r$)$t$)$t$=1$nPaymentt$(1+$r$)$t$.$

The duration formula$$implies that if interest rates increase, duration will$.$ The duration gap formula$$implies that, ceteris paribus, the gap will increase, if the interest rate change affects the value of the bank's assets$$than it affects the value of its liabilities.