SOA Exam FM UPDATED ACTUAL Exam
Questions and CORRECT Answers
Value of $1.00 in a fund at a given time
Given by accumulation function a(t)
Note that a(0) = 1
Amount function: A_k(t) = k * a(t); represents value of investment of k dollars - CORRECT
ANSWER - Accumulated Value, Accumulation Function, Amount Function
i_t = [A(t) - A(t - 1)]/A(t - 1)
Note that A(t) = (1 + i_t)A(t - 1) and
A(t) = k prod_{n = 1}^t (1 + i_n) - CORRECT ANSWER - Effective Rate of Interest
A(t) = k(1 + it)
i_t = i/[1 + i(t - 1)] - CORRECT ANSWER - Simple interest
A(t) = k(1 + i)^t
i_t = i - CORRECT ANSWER - Compound Interest
Present Value: PV_k(t) = 1/A_k(t); represents present value of k dollars after t years/periods.
Discount rate is v_t = 1/(1 + i_t) - CORRECT ANSWER - Present Value
d_t = [A(t) - A(t - 1)]/A(t)
Note: v = 1 - d, i - d = id - CORRECT ANSWER - Effective Rate of Discount
Given nominal interest rate i^(n), (1 + i^(n)/n)^n = 1 + i
Given nominal discount rate d^(n), (1 - d^(n)/n)^n = 1 - d
Note: n is number of compound periods per year - CORRECT ANSWER - Nominal
Interest Rate and Nominal Discount Rate
, del = D a(t) / a(t) = D [ ln(a(t)) ] - CORRECT ANSWER - Force of Interest
del = ln(1 + i) = - ln(1 - d); del = i^(infty) = lim i^(n) = d^(infty) - CORRECT ANSWER -
Constant Force of Interest
e^x = sum_0 x^n/n!
ln(1 + x) = sum_1 (-1)^(n+1) x^n/n - CORRECT ANSWER - Useful Taylor Series
PV: (1 - v^n)/i; special notation is a_n | i
AV: [(1 + i)^n - 1]/i; special notation is s_n | i
Relationship: s_n = (1 + i)^n a_n - CORRECT ANSWER - Present and Accumulated
Value of an Annuity Immediate
PV: (1 - v^n)/d; special notation is a**_n | i
AV: [(1 + i)^n - 1]/d; special notation is s**_n | i
Relationships: a**_n = (1 + i)a_n = a_{n - 1} + 1
s**_n = (1 + i)s_n = s_{n + 1} - 1 - CORRECT ANSWER - Present and Accumulated
Value of an Annuity Due
m|a_n means advance 4 years and then do annuity immediate for n years; similar for s, a**, s**
m|a_n = m+1|a**_n = a_{m + n} - a_m
Similar for s, s** - CORRECT ANSWER - Deferred Annuity Notation
Annuity with infinite payments; can be immediate and due
PV for immediate = a_\infty = 1/i
PV for due = a**_\infty = 1/d - CORRECT ANSWER - Perpetuity
a_2n / a_n = 1 + v^n
Questions and CORRECT Answers
Value of $1.00 in a fund at a given time
Given by accumulation function a(t)
Note that a(0) = 1
Amount function: A_k(t) = k * a(t); represents value of investment of k dollars - CORRECT
ANSWER - Accumulated Value, Accumulation Function, Amount Function
i_t = [A(t) - A(t - 1)]/A(t - 1)
Note that A(t) = (1 + i_t)A(t - 1) and
A(t) = k prod_{n = 1}^t (1 + i_n) - CORRECT ANSWER - Effective Rate of Interest
A(t) = k(1 + it)
i_t = i/[1 + i(t - 1)] - CORRECT ANSWER - Simple interest
A(t) = k(1 + i)^t
i_t = i - CORRECT ANSWER - Compound Interest
Present Value: PV_k(t) = 1/A_k(t); represents present value of k dollars after t years/periods.
Discount rate is v_t = 1/(1 + i_t) - CORRECT ANSWER - Present Value
d_t = [A(t) - A(t - 1)]/A(t)
Note: v = 1 - d, i - d = id - CORRECT ANSWER - Effective Rate of Discount
Given nominal interest rate i^(n), (1 + i^(n)/n)^n = 1 + i
Given nominal discount rate d^(n), (1 - d^(n)/n)^n = 1 - d
Note: n is number of compound periods per year - CORRECT ANSWER - Nominal
Interest Rate and Nominal Discount Rate
, del = D a(t) / a(t) = D [ ln(a(t)) ] - CORRECT ANSWER - Force of Interest
del = ln(1 + i) = - ln(1 - d); del = i^(infty) = lim i^(n) = d^(infty) - CORRECT ANSWER -
Constant Force of Interest
e^x = sum_0 x^n/n!
ln(1 + x) = sum_1 (-1)^(n+1) x^n/n - CORRECT ANSWER - Useful Taylor Series
PV: (1 - v^n)/i; special notation is a_n | i
AV: [(1 + i)^n - 1]/i; special notation is s_n | i
Relationship: s_n = (1 + i)^n a_n - CORRECT ANSWER - Present and Accumulated
Value of an Annuity Immediate
PV: (1 - v^n)/d; special notation is a**_n | i
AV: [(1 + i)^n - 1]/d; special notation is s**_n | i
Relationships: a**_n = (1 + i)a_n = a_{n - 1} + 1
s**_n = (1 + i)s_n = s_{n + 1} - 1 - CORRECT ANSWER - Present and Accumulated
Value of an Annuity Due
m|a_n means advance 4 years and then do annuity immediate for n years; similar for s, a**, s**
m|a_n = m+1|a**_n = a_{m + n} - a_m
Similar for s, s** - CORRECT ANSWER - Deferred Annuity Notation
Annuity with infinite payments; can be immediate and due
PV for immediate = a_\infty = 1/i
PV for due = a**_\infty = 1/d - CORRECT ANSWER - Perpetuity
a_2n / a_n = 1 + v^n
