Glossary of notation

Symbol Chapter Description
\(a(t)\) 1 Time-Value of Money accumulation function
\(a^{-1}(t)\) 1 Time-Value of Money discount function
\(a_{\enclose{actuarial}{n}}\) 2 Annuities present value of an \(n\)-period annuity-immediate
\(\ddot{a}_{\enclose{actuarial}{n}}\) 2 Annuities present value of an \(n\)-period annuity-due
\(a_{\enclose{actuarial}{n}}^{(m)}\) 2 Annuities present value of an \(n\)-period annuity-immediate payable \(m\)thly
\(\ddot{a}_{\enclose{actuarial}{n}}^{(m)}\) 2 Annuities present value of an \(n\)-period annuity-due payable \(m\)thly
\(\bar{a}_{\enclose{actuarial}{n}}\) 2 Annuities present value of an \(n\)-period continuous annuity
\(a_{\enclose{actuarial}{\infty}}\) 2 Annuities present value of a perpetuity-immediate
\(\ddot{a}_{\enclose{actuarial}{\infty}}\) 2 Annuities present value of a perpetuity-due
\(A\) 5 Asset-Liability Management amount in fund at beginning of year
\(A(t)\) 1 Time-Value of Money amount function
\(B\) 5 Asset-Liability Management amount in fund at end of year
\(B^\prime_k\) 5 Asset-Liability Management fund balance at time \(t_k\)
\(B^P_t\) 3 Loans prospective loan balance at time \(t\)
\(B^R_t\) 3 Loans retrospective loan balance at time \(t\)
\(C\) 4 Bonds Redemption amount of a bond
\(d\) 1 Time-Value of Money effective rate of discount
\(d^{(m)}\) 1 Time-Value of Money nominal rate of discount convertible \(m\)thly
\((Da)_{\enclose{actuarial}{n}}\) 2 Annuities present value of a decreasing annuity
\((Ds)_{\enclose{actuarial}{n}}\) 2 Annuities accumulated value of a decreasing annuity
\(F\) 4 Bonds Face amount or par value of a bond
\(Fr\) 4 Bonds Coupon amount of a bond
\(g=\large{\frac{Fr}{C}}\) 4 Bonds Adjusted coupon rate of a bond
\(i\) 1 Time-Value of Money effective rate of interest
\(i^{(m)}\) 1 Time-Value of Money nominal rate of interest convertible \(m\)thly
\(I\) 1 Time-Value of Money amount of interst earned during period
\((Ia)_{\enclose{actuarial}{n}}\) 2 Annuities present value of an increasing annuity
\((Is)_{\enclose{actuarial}{n}}\) 2 Annuities accumulated value of an increasing annuity
\((Ia)_{\enclose{actuarial}{\infty}}\) 2 Annuities present value of an increasing perpetuity
\(i\) 1 Time-Value of Money rate of interest (alternative notation to \(i\))
\(L\) 3 Loans original loan amount
\(\text{MacCon}\) 5 Asset-Liability Management Macaulay convexity
\(\text{MacDur}\) 5 Asset-Liability Management Macaulay duration
\(\text{ModCon}\) 5 Asset-Liability Management modified convexity
\(\text{ModDur}\) 5 Asset-Liability Management modified duration
\(P\) 4 Bonds Price of a bond (i.e., present value of cash flows)
\(P(i)\) 5 Asset-Liability Management net present value at rate of interest \(i\)
\(r\) 4 Bonds coupon rate of a bond
\(s_{\enclose{actuarial}{n}}\) 2 Annuities accumulated value of an \(n\)-period annuity-immediate
\(\ddot{s}_{\enclose{actuarial}{n}}\) 2 Annuities accumulated value of an \(n\)-period annuity-due
\(s_{\enclose{actuarial}{n}}^{(m)}\) 2 Annuities accumulated value of an \(n\)-period annuity-immediate payable \(m\)thly
\(\ddot{s}_{\enclose{actuarial}{n}}^{(m)}\) 2 Annuities accumulated value of an \(n\)-period annuity-due payable \(m\)thly
\(\bar{s}_{\enclose{actuarial}{n}}\) 2 Annuities accumulated value of an \(n\)-period continuous annuity
\(v\) 1 Time-Value of Money discount factor
\(\delta\) 1 Time-Value of Money force of interest