IC28 FOUNDATION OF ACTUARIAL SCIENCES

IC28 Mock Test Sample 18

This section explains nominal discount rates, effective interest and discount relationships, annuity conversion, and basic probability concepts. It covers formulas connecting nominal discount rates convertible multiple times yearly with effective rates of interest and discount. Practical exercises include bill discounting, money lending, and annuity conversions. The chapter also introduces probability theory, including sample space, mutually exclusive and exhaustive events, and probability calculations using classical and statistical definitions. Examples from card games and mortality data illustrate probability applications. Important properties such as probabilities lying between 0 and 1 and relative frequency interpretation are also discussed for actuarial and statistical understanding.

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1. In Exercise 5 Q.1, given d^(2) = 0.19, d^(4) is found by solving:

a. (1-d^(4)/4)^4 = (1-d^(2)/2)^2
b. d^(4) = 2d^(2)
c. d^(4) = (1-d^(2))^(1/2)
d. d^(4) = d^(2)

2. In Exercise 5 Q.5, the sum of accumulated value at nominal interest and present value at nominal discount over 2 years equals 2.1202. The rate is found by:

a. Solving (1+i/2)^4 + (1-i/2)^4 = 2.1202
b. Direct formula
c. Approximation only
d. Trial and error only

3. In Exercise 5 Q.4, the identity to prove is i/d^(p) = i/i^(p) + i/p. This relates effective i to nominal rates by:

a. Algebra using 1/d^(p) = 1/i^(p) + 1/p scaled by i
b. Calculus
c. Geometric reasoning
d. Trial method

4. Money lender example (Q.3): charges Rs.5 per Rs.100 in advance per quarter. The effective discount rate per quarter is:

a. 5%
b. 20%
c. 21.55%
d. 19.5%

5. In Q.3, the effective rate of interest per annum charged is approximately:

a. 20%
b. 21.55%
c. 19.5%
d. 23%

6. In Exercise 5 Q.13, converting Rs.2400 immediate annual annuity to half-yearly at 8% effective, equivalent half-yearly annual sum equals:

a. 2400 × a_n / a_n^(2)
b. 2400 × i / i^(2)
c. 2400 × 2
d. 2400 / 2

7. What is meant by 'gross interest' for a life office?

a. Net interest plus tax paid
b. Net interest minus tax
c. Premium income
d. Interest before expenses

8. What is the title of Chapter 6?

a. Statistics
b. Probability
c. Combinatorics
d. Random Variables

9. The probability of an event is best described as:

a. A guaranteed outcome
b. The measure of chance that the event will occur
c. A purely subjective belief
d. A future certainty

10. What is a 'sample space'?

a. A subset of outcomes
b. The set of all possible outcomes of an experiment
c. Only the favourable outcomes
d. Only the impossible outcomes

11. Two events are mutually exclusive if:

a. They occur together always
b. They cannot occur at the same time
c. Their probabilities sum to less than 1
d. They are independent

12. Two events are non-mutually exclusive if:

a. They have one or more common outcomes
b. Their union has zero probability
c. They are independent
d. Their intersection is empty

13. What does 'exhaustive events' mean?

a. Events whose union covers the entire sample space
b. Events that occur infinitely
c. Events with high probability
d. Events that exhaust resources

14. Per formula (6.1), the probability P of an event is:

a. Number of favourable events / Number of mutually exclusive and exhaustive events
b. Total events / Favourable events
c. Number of trials / Number of successes
d. Always 1

15. From a 52-card pack, the probability of drawing a diamond is:

a. 1/13
b. 1/4
c. 1/26
d. 1/2

16. From a 52-card pack, the probability of drawing a king is:

a. 1/13
b. 1/4
c. 1/52
d. 4/13

17. From a 52-card pack, the probability of drawing a red card is:

a. 1/4
b. 1/13
c. 1/2
d. 13/52

18. In the statistical definition of probability, the relative frequency n/N:

a. Is exactly the probability
b. Tends to a limiting value as N becomes large
c. Is independent of N
d. Is always 1/2

19. If 13 die out of 10,000 lives aged 35 in a year, the death rate q35 is approximately:

a. 0.0013
b. 0.013
c. 0.13
d. 1.3

20. Per property (6.2), the probability of any event lies between:

a. 0 and 1
b. -1 and 1
c. 0 and infinity
d. Any real values