|
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
|