Actuarial Mathematics MCQs
\[
\textbf{Difficult MCQs on Actuarial Mathematics with Answers}
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\[
\textbf{Q1: What is the actuarial present value (APV) of a life insurance policy?}
\]
\[
\text{(A) } \text{The present value of future premiums}
\]
\[
\text{(B) } \text{The present value of future benefits}
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\[
\text{(C) } \text{The present value of the future cash flows, considering mortality rates and interest}
\]
\[
\text{(D) } \text{The sum of premiums paid over the policy term}
\]
\[
\textbf{Answer: (C) The present value of the future cash flows, considering mortality rates and interest}
\]
\[
\textbf{Q2: In a compound interest model, what is the formula to calculate the accumulated value of an annuity due after t years?}
\]
\[
\text{(A) } \text{A = P \left( \frac{(1 + r)^t – 1}{r} \right)}
\]
\[
\text{(B) } \text{A = P \left( \frac{(1 + r)^t}{r} \right)}
\]
\[
\text{(C) } \text{A = P \left( \frac{(1 + r)^t – 1}{r} \right) (1 + r)}
\]
\[
\text{(D) } \text{A = P \left( \frac{1 – (1 + r)^{-t}}{r} \right)}
\]
\[
\textbf{Answer: (C) A = P \left( \frac{(1 + r)^t – 1}{r} \right) (1 + r)}
\]
\[
\textbf{Q3: In actuarial science, what is the ‘force of mortality’?}
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\[
\text{(A) } \text{The probability of death within a specific age range.}
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\[
\text{(B) } \text{The rate of change in the mortality rate over time.}
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\[
\text{(C) } \text{The instantaneous rate of mortality at a given time.}
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\[
\text{(D) } \text{The proportion of the population that dies in a given year.}
\]
\[
\textbf{Answer: (C) The instantaneous rate of mortality at a given time.}
\]
\[
\textbf{Q4: In the context of a life insurance policy, which of the following is the best description of the term ‘mortality rate’?}
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\[
\text{(A) } \text{The probability that an individual will die within a year.}
\]
\[
\text{(B) } \text{The probability that an individual will live for a certain number of years.}
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\[
\text{(C) } \text{The number of deaths per year in a population divided by the number of people at risk.}
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\[
\text{(D) } \text{The probability that an individual will die before reaching the maximum age.}
\]
\[
\textbf{Answer: (C) The number of deaths per year in a population divided by the number of people at risk.}
\]
\[
\textbf{Q5: What does the actuarial symbol \(a_{\overline{n}}^{(m)}\) represent?}
\]
\[
\text{(A) } \text{The present value of a life insurance policy after n years with monthly payments.}
\]
\[
\text{(B) } \text{The present value of an annuity that pays m times a year over n years.}
\]
\[
\text{(C) } \text{The accumulated value of an annuity with m payments made annually over n years.}
\]
\[
\text{(D) } \text{The present value of a policy with a term of n years, paid monthly over m years.}
\]
\[
\textbf{Answer: (B) The present value of an annuity that pays m times a year over n years.}
\]
\[
\textbf{Q6: In the context of pension plans, which of the following is a characteristic of the ‘vested benefit’?}
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\[
\text{(A) } \text{The amount an employee is entitled to receive from a pension plan if they leave the company.}
\]
\[
\text{(B) } \text{The employer’s contribution to the pension plan.}
\]
\[
\text{(C) } \text{The projected benefit an employee will receive at retirement.}
\]
\[
\text{(D) } \text{The interest earned on the contributions made to the pension plan.}
\]
\[
\textbf{Answer: (A) The amount an employee is entitled to receive from a pension plan if they leave the company.}
\]
\[
\textbf{Q7: The rate of return used in actuarial mathematics to discount future cash flows is often referred to as the:}
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\[
\text{(A) } \text{interest rate.}
\]
\[
\text{(B) } \text{discount rate.}
\]
\[
\text{(C) } \text{mortality rate.}
\]
\[
\text{(D) } \text{inflation rate.}
\]
\[
\textbf{Answer: (B) Discount rate.}
\]
\[
\textbf{Q8: What is the formula for calculating the actuarial present value (APV) of a single payment made t years in the future at interest rate i?}
\]
\[
\text{(A) } \text{APV = P (1 + i)^t}
\]
\[
\text{(B) } \text{APV = P (1 + i)^{-t}}
\]
\[
\text{(C) } \text{APV = P (1 + i)^{-t} \cdot (1 + q)^t}
\]
\[
\text{(D) } \text{APV = P (1 – i)^t}
\]
\[
\textbf{Answer: (B) APV = P (1 + i)^{-t}}
\]
\[
\textbf{Q9: In the context of an actuarial life table, what does the symbol \(q_x\) represent?}
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\[
\text{(A) } \text{The probability of surviving from age x to age x+1.}
\]
\[
\text{(B) } \text{The probability that a person aged x will die before reaching age x+1.}
\]
\[
\text{(C) } \text{The number of people alive at age x.}
\]
\[
\text{(D) } \text{The expected number of years lived by a person aged x.}
\]
\[
\textbf{Answer: (B) The probability that a person aged x will die before reaching age x+1.}
\]
\[
\textbf{Q10: In actuarial mathematics, what is the primary purpose of using the principle of equivalence?}
\]
\[
\text{(A) } \text{To determine the net premium for a life insurance policy.}
\]
\[
\text{(B) } \text{To calculate the future value of annuities.}
\]
\[
\text{(C) } \text{To determine the relationship between premiums and benefits in an insurance contract.}
\]
\[
\text{(D) } \text{To estimate the duration of a pension plan.}
\]
\[
\textbf{Answer: (C) To determine the relationship between premiums and benefits in an insurance contract.}
\]