IC28 Mock Test Sample 14

This section explains advanced annuity and loan concepts used in actuarial science and financial mathematics. It covers level, increasing, decreasing, and varying annuities, loan repayment methods, sinking funds, capital redemption policies, paid-up values, and surrender values. The chapter also explains formulas for principal outstanding, interest and capital portions of instalments, geometric and arithmetic progression annuities, and valuation under varying interest rates. Examples demonstrate calculations involving loans, bonds, redemption policies, quarterly and half-yearly payments, and effective interest rates. These concepts are essential for understanding financial planning, insurance mathematics, investment valuation, and structured loan repayment techniques in practice.

Q1. Per (4.26), the proportionate paid-up value t/n is less than the theoretical $a_t/a_n$ because:

a) Of expense loadings
b) $a_t/t > t/n$ for $n > t$
c) Premiums increase
d) The interest rate is high

Q2. What are 'office premiums'?

a) Net premiums paid by office staff
b) Premiums calculated with provision for expenses
c) Tax-deductible premiums
d) Risk-free premiums

Q3. Per (4.27), the office premium P for a Capital Redemption Policy is given by:

a) A complex expression involving $Sv^n$ , expenses and $a_n$
b) Just $S/a_n$
c) $i + 1/s_n$
d) $S \times v^n$ only

Q4. What is 'Surrender Value'?

a) The value paid when policy is discontinued
b) The face value of the policy
c) The accumulated bonus
d) Tax credit on policy

Q5. In Example 9, the office premium for Rs. 20000 over 15 years is approximately:

a) Rs. 500
b) Rs. 608.23
c) Rs. 700
d) Rs. 800

Q6. In Example 10, annual premium for a 20-year Capital Redemption Policy is approximately:

a) Rs. 400
b) Rs. 455.94
c) Rs. 500
d) Rs. 600

Q7. In Example 10(b), the policy value just before the 9th premium is approximately:

a) Rs. 3000
b) Rs. 5005.31
c) Rs. 6000
d) Rs. 4000

Q8. In Example 10(c), the paid-up sum assured is approximately:

a) Rs. 5000
b) Rs. 11273
c) Rs. 15000
d) Rs. 8000

Q9. In Example 11, surrender value is calculated using accumulation at:

a) 6% effective
b) 7% effective
c) 6% nominal half-yearly
d) 8% effective

Q10. In Example 12(a), present value of Rs. 200 yearly for 16 years is approximately:

a) Rs. 1500
b) Rs. 1889.32
c) Rs. 2200
d) Rs. 2500

Q11. In Example 12(a), present value of Rs. 480 quarterly for 12 years is approximately:

a) Rs. 3000
b) Rs. 3911.16
c) Rs. 4500
d) Rs. 2500

Q12. In Example 12(a), present value of Rs. 300 every 3 years for 15 years is approximately:

a) Rs. 2000
b) Rs. 2549.72
c) Rs. 3000
d) Rs. 1800

Q13. In Example 13, value of A is approximately:

a) Rs. 100
b) Rs. 543.54
c) Rs. 750
d) Rs. 200

Q14. In Example 16, X must pay Y the true sum approximately:

a) Rs. 1500
b) Rs. 2112
c) Rs. 2500
d) Rs. 3000

Q15. In Example 17, equated monthly instalment is approximately:

a) Rs. 800
b) Rs. 958.30
c) Rs. 1100
d) Rs. 1500

Q16. In Example 17, including collection fee, effective annual rate is approximately:

a) 12.0%
b) 15.2%
c) 18.0%
d) 10.5%

Q17. In Example 18, effective rate is approximately:

a) 3.08%
b) 5.0%
c) 8.0%
d) 6.5%

Q18. In Example 19, alternative (a) paid-up value:

a) Increases with t
b) Decreases with t
c) Constant
d) Independent of t

Q19. In Example 19, alternative (a) operates for which range of t?

a) $1 \le t \le 5$
b) $3 \le t \le 20$
c) $5 \le t \le 15$
d) $20 \le t \le 25$

Q20. In Example 20, the identity factorizes into:

a) Sum form
b) Product form
c) Continued fractions
d) Integral

Click here to View Answer

Click Here To Read More