IC28 Mock Test Sample 4
Advanced annuity concepts include annuity due, deferred annuity due, accumulated values, and perpetuities. Annuity due payments occur at the beginning of each period, while deferred annuities begin after a waiting period. Symbols such as s̈n|, ä n|, and m|ä n| represent accumulated and present values of different annuity types. Relationships between present value and accumulated value formulas help simplify actuarial calculations. Perpetuities are annuities with infinite payments and are widely used in finance and valuation models. Immediate perpetuities pay at period-end, while perpetuity due payments are made in advance. These concepts are important in insurance, pensions, investments, and actuarial financial mathematics.
Q1. s̈n| in terms of sn| is:
a) s̈n| = (1+i) sn|
b) s̈n| = v sn|
c) s̈n| = sn| − 1
d) s̈n| = sn+1| − 1
Q2. An equivalent expression for s̈n| is:
a) sn+1| − 1
b) sn| − 1
c) sn−1|
d) ān| + 1
Q3. s̈14| at 6% in Example 13, given s15| = 14.9716, equals:
a) 13.9716
b) 14.9716
c) 15.9716
d) 12.9716
Q4. The present value of a deferred annuity due of 1 p.a. for n years with deferment m years is denoted by:
a) m|ä n|
b) ä n|
c) m|ān|
d) s̈n|
Q5. m|ä n| equals:
a) vm ä n|
b) vm−1 ān|
c) Both A and B
d) vm+1 ān|
Q6. m|ä n| can also be written as:
a) am+n−1| − am−1|
b) am+n| − am|
c) sm+n| − sm|
d) ä n| + am|
Q7. 5|ä10| at 6% equals:
a) a14| − a4|
b) a15| − a5|
c) ä10|
d) 5.8299
Q8. The accumulated value of a deferred annuity due of 1 p.a. for n years certain at the end of m+n years is denoted by:
a) m|s̈n|
b) s̈n|
c) m|sn|
d) sn|
Q9. m|s̈n| equals (equation 2.22 / 2.23):
a) s̈n|
b) (1+i) sn|
c) Both A and B
d) sm+n|
Q10. m|s̈n| can also be expressed as:
a) sn+1| − 1
b) sm+n| − 1
c) sm+n| − sm−1|
d) sm|
Q11. 5|s̈14| at 6% equals:
a) 13.9716
b) 14.9716
c) 15.9716
d) 6.0000
Q12. An annuity whose payments continue forever is called:
a) Level annuity
b) Annuity due
c) Perpetuity
d) Deferred annuity
Q13. If the first payment of a perpetuity is at the end of the first year, it is an:
a) Immediate perpetuity in arrear
b) Perpetuity due
c) Deferred perpetuity
d) Continuous perpetuity
Q14. The present value of an immediate perpetuity in arrear of 1 p.a. is denoted by:
a) a∞|
b) ä∞|
c) sn|
d) m|ān|
Q15. The present value of an immediate perpetuity in arrear of 1 p.a. equals:
a) 1/i
b) 1/d
c) (1+i)/i
d) (1−v)/i
Q16. The present value of a perpetuity due of 1 p.a. equals:
a) 1/i
b) 1/d
c) (1−vn)/d
d) (i+1)/i
Q17. For a deferred perpetuity with first payment one year after m years, the present value is:
a) vm/i
b) vm/d
c) vm · ä∞|
d) 1/i
Q18. For a deferred perpetuity due, the present value equals:
a) vm/d
b) vm−1/i
c) Both A and B
d) 1/i
Q19. In Example 16, Mr. Shah is entitled to Rs. 1800 p.a. ad infinitum, first payment at end of year 6. PV at 6% is approximately:
a) Rs. 30,000
b) Rs. 22,417.80
c) Rs. 18,000
d) Rs. 1,800
Q20. In Example 17, with effective rate 8% p.a., the nominal rate convertible half-yearly i(2) satisfies:
a) (1 + i(2)/2)² = 1.08
b) i(2) = 8%
c) i(2) = 4%
d) i(2) = 16%
