IC28 Mock Test Sample 7
Foundation of Actuarial Sciences explains the principles of interest, discounting, annuities, perpetuities, and loan valuation. It covers present value and accumulated value calculations using compound interest and actuarial symbols such as a n ∣ , s n ∣ , and annuity-due functions. The chapter also introduces deferred annuities, perpetuities, increasing annuities, and varying payment streams. Students learn how actuarial formulas help evaluate loans, investments, instalments, pensions, and financial contracts. Practical applications include educational loans, debentures, quarterly and half-yearly payment systems, and valuation at different frequencies of conversion. These concepts form the mathematical foundation for insurance, finance, and actuarial decision-making.
Q1. In Exercise 2.2 Q.3, an educational loan of four annual amounts of Rs. 800 each at start of years 1 to 4, repaid as lump sum at end of 10 years at 6%, has lump sum equal to:
a) 800 s̈̅4| (1+i)^6
b) 800 a̅4|
c) 800 s̅4|
d) 800 only
Q2. For Exercise 2.2 Q.4, if the loan in Q.3 is repaid by 10 equal annual payments first being at end of year 10, those payments form a deferred annuity. The present value of which equals the loan PV:
a) 9|a̅10| · X = loan PV
b) a̅10| · X = loan PV
c) ä̅10| · X = loan PV
d) X = loan PV
Q3. In Exercise 2.1 Q.2, A is entitled to Rs. 200 p.a. for 4 years and Rs. 150 p.a. for next 5 years at 7%. The PV equals:
a) 200 a̅4| + 150 (a̅9| − a̅4|)
b) 200 a̅9|
c) 350 a̅9|
d) 150 a̅4| + 200 a̅5|
Q4. In Exercise 2.2 Q.6, PV at 6% involves:
a) Immediate annuity, deferred annuity, and discounting
b) Only annuity calculations
c) Only discounting
d) Only accumulated value
Q5. In Exercise 2.2 Q.7, a person receives Rs. 350 p.a. for 8 years and Rs. 250 p.a. for next 6 years; first sum due at end of year 6 from now. PV at 5% requires:
a) Both annuities to be deferred
b) Only one to be deferred
c) No deferment
d) Annuity due
Q6. In Exercise 2.2 Q.8, the value of an immediate annuity of Rs. 100 p.a. for 9 years at 8% effective is computed as:
a) 100 4|a̅9|
b) 100 a̅9|
c) 100 5|a̅9|
d) 100 ä̅9|
Q7. In the relation ä̅n| = (1 − v^n)/(d), what does d represent?
a) Rate of discount
b) Rate of interest
c) Period of deferment
d) Number of payments
Q8. For an annuity, the relationship 1 − v^n = d ä̅n| implies that an investment of 1:
a) Yields a perpetuity-due of d
b) Yields a perpetuity-arrear of i
c) Yields nothing
d) Doubles in value
Q9. For a level annuity, the equality a̅n| · i + v^n = 1 shows:
a) A unit yields interest i at end of each year for n years and 1 returned at end
b) A unit yields interest only
c) Annuities are unrelated to interest
d) Standard discounting
Q10. The accumulated value formula s̅n| = 1 + (1+i) + (1+i)^2 + … has first term 1 because:
a) The last payment has earned no interest
b) All payments earn interest
c) The first payment is at time 0
d) The annuity is perpetual
Q11. Equation a̅n| → 1/i as n → ∞ provides a useful check that:
a) Annuity values are bounded by perpetuity values
b) Annuity values are unbounded
c) Higher rates give higher PV
d) Time has no effect
Q12. For computing the half-yearly instalment in Exercise 2.1 Q.3, the cash price equation is:
a) 10000 = 2000 + X a̅5| at 6% per half-year
b) 10000 = X a̅5|
c) 10000 = 2000 + X s̅5|
d) 10000 = 5X
Q13. Variable annuities are those in which:
a) All payments are equal
b) Periodical payments vary
c) No payments are made
d) Payments continue forever
Q14. For a general variable annuity, the present value can always be obtained by:
a) Multiplying each payment by appropriate discount or accumulation factors and summing
b) Using a̅n| alone
c) Using only level annuity tables
d) Discounting only one payment
Q15. In an immediate increasing annuity (Ia)̅n|, the payment at the end of the kth time period is:
a) 1
b) k
c) k²
d) v^k
Q16. The present value of an immediate increasing annuity (Ia)̅n| is given by:
a) (ä̅n| − nv^n)/i
b) (a̅n| − nv^n)/d
c) (1 − v^n)/i
d) n · a̅n|
Q17. An equivalent form of (Ia)̅n| is:
a) a̅n| + (a̅n| − nv^n)/i
b) a̅n| + nv^n
c) ä̅n| + nv^n
d) a̅n|/i
Q18. In Example 1, (Ia)̅10| at 8% equals:
a) 32.6876
b) 6.7101
c) 10
d) 100
Q19. The present value of an immediate increasing perpetuity (Ia)̅∞| equals:
a) 1/i
b) 1/i + 1/i²
c) 1/d²
d) 1/i²
Q20. In an increasing annuity-due (Iä)̅n|, the payment at the start of the kth year is:
a) 1
b) k
c) k−1
d) v^k
