IC28 Mock Test Sample 3
Deferred annuities are annuities where payments begin after a waiting period called the deferment period. Present value and accumulated value calculations are important in actuarial science for valuing pensions, insurance benefits, and investments. Symbols such as m|ān|, ä n|, and s̈n| are used for deferred annuities, annuity due, and accumulated annuity values. The short method helps simplify evaluation of annuity expressions involving powers of interest accumulation. Immediate annuities are paid in arrears, while annuity due payments occur in advance. Relationships between present values, accumulated values, and discount factors are widely used in actuarial mathematics and financial decision-making.
Q1. The short method for evaluating (1+i)t ān| requires that:
a) t must be greater than n
b) t must be less than n
c) t must equal n
d) No restriction on t
Q2. The present value of a deferred immediate annuity of 1 p.a. for n years with deferment period m years is denoted by:
a) ān|
b) m|ān|
c) ä n|
d) sn|
Q3. The formula for m|ān| in terms of vm and ān| is:
a) vm ān|
b) (1+i)m ān|
c) vm sn|
d) ān|/vm
Q4. An alternative expression for m|ān| is:
a) am+n| − am|
b) am| − an|
c) sm+n| − sm|
d) an| + am|
Q5. In Example 8, the present value of 6 payments of Rs. 200 p.a., the first being at the end of 8 years, at 6% is:
a) Rs. 3.2703
b) 200 × 3.2703
c) Rs. 8.8527
d) Rs. 5.5824
Q6. In Example 9, present value at 6% of 4 payments of Rs. 200 followed by 7 of Rs. 350 is:
a) Rs. 2240.65
b) Rs. 1500.00
c) Rs. 3000.00
d) Rs. 2000.00
Q7. The present value of Rs. 100 p.a. for 5 years deferred 5 years at 6% equals:
a) Rs. 339.22
b) Rs. 500.00
c) Rs. 200.00
d) Rs. 400.00
Q8. In Example 11, with annuity of Rs. 500 for first 10 years and Rs. 300 for next 5 years at 4%, the present value is:
a) Rs. 4055.45
b) Rs. 902.25
c) Rs. 4957.70
d) Rs. 5000.00
Q9. The accumulated value of a deferred annuity of 1 p.a. for n years with deferment period m years, evaluated at the end of m+n years, equals:
a) sn|
b) sm+n|
c) sm+n| − sm|
d) vm sn|
Q10. For an immediate annuity of 1 p.a. for n years certain, the accumulated value m years after annuity payments have ceased is:
a) sn|
b) (1+i)m sn|
c) vm sn|
d) sm+n| − sm|
Q11. The relation (1+i)m sn| = sm+n| − sm| is given by which equation?
a) (2.10)
b) (2.11)
c) (2.12)
d) (2.15)
Q12. To evaluate (1+i)t ān| when t = n, the result is:
a) ān|
b) sn|
c) vn ān|
d) ä n|
Q13. To evaluate (1+i)t ān| when t > n, write t = m+n; the result is:
a) (1+i)m sn|
b) sn|
c) ān|
d) ä n|
Q14. vt ān| represents:
a) Accumulated value of deferred annuity
b) Present value of a deferred annuity for n years deferred t years
c) Annuity due for n years
d) Perpetuity
Q15. vt sn| when t = n equals:
a) ān|
b) sn|
c) ä n|
d) 1
Q16. vt sn| when t > n, writing t = m+n, equals:
a) vm ān|
b) sn|
c) ān| − vm
d) m|ān|
Q17. The present value of an annuity due of 1 p.a. for n years certain equals:
a) (1−vn)/d
b) (1−vn)/i
c) ((1+i)n−1)/d
d) 1/i
Q18. In equation (2.14), ä n| = 1 + ān−1| because:
a) First payment is immediate; remaining (n−1) form an immediate annuity
b) First payment is at end of year
c) All payments are deferred
d) Annuity is perpetual
Q19. ä10| at 6%, given ā9| = 6.8017, equals:
a) 7.8017
b) 6.8017
c) 8.0000
d) 10.000
Q20. The accumulated value of an annuity due of 1 p.a. for n years at the end of n years is denoted by:
a) sn|
b) s̈n|
c) ä n|
d) m|sn|
