ACTUARIAL SCIENCE 303 QUESTIONS
AND VERIFIED ANSWERS|100%
CORRECT|GRADE A+
accumulation function simple interest - ANSWER 1 + i * t
Accumulated Amount - ANSWER A(t) = A(0) * a(t)
Accumulation Function Compound Interest - ANSWER (1 + i) ^ t
rate of discount - ANSWER [A(t) - A(t - 1)] / A(t)
present value v = - ANSWER 1 / (1 + i)
To take the value back to time 0 - ANSWER A(t) * (v ^ t)
In terms of discount, i = - ANSWER d / (1 - d)
In terms of interest, d = - ANSWER i / (1 + i)
a(6,10) is the same as - ANSWER a(4)
In terms of accumulated value, 1 - d = - ANSWER A(n) / A(n + 1)
In terms of accumulated value, 1 + i = - ANSWER A(n + 1) / A(n)
In terms of i, 1 - d = - ANSWER 1 / (1 + i)
In terms of d, 1 + i = - ANSWER 1 / (1 - d)
, (1 + j) ^ p = - ANSWER Annual Effective interest rate i
Force of interest equation - ANSWER δt = Derivative a(t) / a(t)
In words, the force of interest is - ANSWER The instantaneous change in the accumulation function
For simple interest, as t increases, δ ___ - ANSWER Decreases
jmontly accumulation function - ANSWER (1 + jmonthly) ^ 12t
Force of interest accumulation function - ANSWER e ^ integral from 0 to t(δs)
Constant force of interest accumulation function - ANSWER e ^ δt
i ^ (m) in words - ANSWER The nominal annual rate of interest convertible (m) times per year
i ^ (m) / m - ANSWER mthly effective rate of interest
the limit as m approaches infinity of i ^ m = - ANSWER δ
d ^ (p) / p - ANSWER pthly effective rate of discount
in terms of i, (1 + (i ^ m) / m) ^ m = - ANSWER 1 + i, annual effective rate of interest
in terms of d, (1 / (1-(d ^ p/ p)) ^ p) - ANSWER
In terms of d, v = - ANSWER 1 - d
AND VERIFIED ANSWERS|100%
CORRECT|GRADE A+
accumulation function simple interest - ANSWER 1 + i * t
Accumulated Amount - ANSWER A(t) = A(0) * a(t)
Accumulation Function Compound Interest - ANSWER (1 + i) ^ t
rate of discount - ANSWER [A(t) - A(t - 1)] / A(t)
present value v = - ANSWER 1 / (1 + i)
To take the value back to time 0 - ANSWER A(t) * (v ^ t)
In terms of discount, i = - ANSWER d / (1 - d)
In terms of interest, d = - ANSWER i / (1 + i)
a(6,10) is the same as - ANSWER a(4)
In terms of accumulated value, 1 - d = - ANSWER A(n) / A(n + 1)
In terms of accumulated value, 1 + i = - ANSWER A(n + 1) / A(n)
In terms of i, 1 - d = - ANSWER 1 / (1 + i)
In terms of d, 1 + i = - ANSWER 1 / (1 - d)
, (1 + j) ^ p = - ANSWER Annual Effective interest rate i
Force of interest equation - ANSWER δt = Derivative a(t) / a(t)
In words, the force of interest is - ANSWER The instantaneous change in the accumulation function
For simple interest, as t increases, δ ___ - ANSWER Decreases
jmontly accumulation function - ANSWER (1 + jmonthly) ^ 12t
Force of interest accumulation function - ANSWER e ^ integral from 0 to t(δs)
Constant force of interest accumulation function - ANSWER e ^ δt
i ^ (m) in words - ANSWER The nominal annual rate of interest convertible (m) times per year
i ^ (m) / m - ANSWER mthly effective rate of interest
the limit as m approaches infinity of i ^ m = - ANSWER δ
d ^ (p) / p - ANSWER pthly effective rate of discount
in terms of i, (1 + (i ^ m) / m) ^ m = - ANSWER 1 + i, annual effective rate of interest
in terms of d, (1 / (1-(d ^ p/ p)) ^ p) - ANSWER
In terms of d, v = - ANSWER 1 - d
