FM for Actuaries

Table 1.3:
Summary of accumulated value and present value formulas (all rates quoted per year)
Freq of Rate of Future value Present value of
Accumulation conversion interest or of 1 at time t 1 due at time t Equations
method per year discount (in years): a(t) (in years): 1/a(t) in book Remarks
Compound 1 r (= i) (1 + r) t (1 + r) −t (1.4) also applies to
interest non-integer t>0
[
Compound m r (m)
interest
1+ r(m)
m
] mt [
1+ r(m)
m
] −mt
(1.6) m>1 if compounding is
more frequent than annually
Compound ∞ ¯r e¯rt e −¯rt (1.9) ¯r is the constant
interest
force of interest δ
Compound 1 d (1 − d) −t (1 − d) t (1.4), (1.7)
discount
1 − d(m) 1 − d(m)
m
m
Compound m d (m) [ ] −mt [ ] mt
(1.19) m>1 for loan period
discount
shorter than 1 year
Simple r 1+rt (1 + rt) −1 (1.2)
interest
Simple d (1 − dt) −1 1 − dt (1.23)
discount
Interest Accumulation and Time Value of Money 29