IC28 Mock Test Sample 1
Foundation of Actuarial Sciences includes concepts of interest, discounting, annuities, and risk management. It explains nominal and effective interest rates, compound and simple interest, present value, and accumulated value calculations. The subject also covers discount rates, frequency of compounding, and financial risks faced by investors. Annuities are regular series of payments that may be level, life, immediate, or annuity-due depending on payment timing and duration. Compound interest increases wealth faster because interest earns additional interest over time. These concepts are essential in insurance, pensions, investments, and financial mathematics, helping actuaries evaluate future liabilities, premiums, and financial decisions accurately and systematically.
Q1. The nominal rate of interest p.a. convertible m times a year is denoted by:
a) i
b) d
c) i(m)
d) vm
Q2. If interest is at 4% p.a. payable half-yearly on Rs. 100, the effective rate p.a. is:
a) 4%
b) 4.04%
c) 4.08%
d) 8%
Q3. The relation between effective rate i and nominal rate i(m) convertible m times a year is:
a) i = (1 + i(m))m − 1
b) i = (1 + i(m)/m)m − 1
c) i = m × i(m)
d) i = i(m)/m
Q4. The effective rate corresponding to a nominal rate of 8% p.a. convertible quarterly is approximately:
a) 8.000%
b) 8.243%
c) 8.160%
d) 7.770%
Q5. The accumulated value of Rs. 200 at 4% p.a. payable quarterly at the end of 5.5 years is:
a) Rs. 200(1.01)22
b) Rs. 200(1.04)5.5
c) Rs. 200(1.04)22
d) Rs. 200(1.01)5.5
Q6. The relation between rate of discount d and present value v is:
a) d = 1 + v
b) d = 1 − v
c) d = v − 1
d) d = v
Q7. The relation v × i = d implies that the rate of discount d equals:
a) Interest on principal 1 for one year
b) Interest on the present value v for one year
c) Future value of i
d) Compound interest over n years
Q8. If the rate of interest is 0.06, the corresponding rate of discount is:
a) 0.0566
b) 0.0600
c) 0.0636
d) 0.0660
Q9. If the rate of discount is 0.08, the corresponding rate of interest is:
a) 0.0800
b) 0.0870
c) 0.0741
d) 0.0869
Q10. Discount d can be regarded as:
a) Interest on (1 + i) a year hence
b) Discount of 1 due a year hence
c) Future value of i
d) Compound amount of v2
Q11. The investor faces the possible risk that:
a) Interest rates will fall
b) The borrower will default on capital and/or interest
c) The lender will withdraw funds
d) The principal will become negative
Q12. If Rs. 100 is invested at 10% p.a. simple interest, the total amount at the end of 3 years is:
a) Rs. 130
b) Rs. 133.10
c) Rs. 103
d) Rs. 300
Q13. Why does compound interest give a higher amount than simple interest over multiple years?
a) Higher rate is always charged
b) Interest itself earns interest in subsequent periods
c) Principal is multiplied by n
d) Tables use different formulas
Q14. For a given rate of interest p.a., as the frequency of conversion m increases:
a) Interest earned decreases
b) Interest earned remains the same
c) Interest earned increases
d) Principal decreases
Q15. The present value of Rs. 500 payable at the end of 4 years and 3 months at 7% p.a. requires evaluating:
a) 500 × v4.25 at 7%
b) 500 × v4 × (1.07)
c) 500 × (1.07)4.25
d) 500 × v0.25
Q16. An annuity with equal payments at regular intervals is called:
a) Variable annuity
b) Level annuity
c) Life annuity
d) Perpetuity
Q17. If annuity payments are made during the life of a person, it is called:
a) Annuity certain
b) Life annuity
c) Annuity due
d) Perpetuity
Q18. If annuity payments are made at the end of each period, they are paid in:
a) Advance
b) Arrears
c) Perpetuity
d) Default
Q19. An annuity in which payments are made at the beginning of each period is called:
a) Immediate annuity
b) Annuity-due
c) Deferred annuity
d) Perpetuity
Q20. An annuity certain of Rs. 1 p.a. payable in arrears for 10 years has its first payment made at:
a) Time 0
b) End of 1st year
c) Beginning of 1st year
d) End of 10th year
