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| rev | Admin | (Created page with "'''Solution: B''' The denominator of the duration is the present value of the annuity <math display = "block"> X\ddot{a}_{\overline{20}|0.02}+4Xv^{20}\ddot{a}_{\overline{30}|2}=78.1729X. </math> The numerator is the time-weighted present value of the annuity. In units of X we need the present value of 0, 1, ..., 19, 80, 84, ..., 196. One way to view this is as four times a 49-year increasing immediate annuity (so payments of 4, 8, ..., 76, 80, 84, ..., 196) less three...") | Nov 20'23 at 13:32 | +796 |