Reference no: EM132276941

Questions -

Q1. The nominal rate of interest is 10% per annum payable p-thly, that is i^(p) = 10%. Calculate the equivalent effective rate of interest per annum for p = 1, 4 and 6.

Q2. The effective rate of interest per annum is 10%, that is i = 0.1. Calculate the equivalent nominal rate of interest per annum, i^(p) for p = 1, 4 and 6.

Q3. The nominal rate of interest is 6% per annum payable half-yearly.

a) What is the effective annual rate of interest earned on this investment?

b) What is the accumulated value of £1,000 after two years?

Q4. Given the effective rate of discount per annum, d = 0.04, find:

a) The equivalent nominal rate of discount per annum convertible:

i) Half-yearly;

ii) Every 4 months;

b) The value of v.

c) Find the equivalent nominal rate of discount per annum convertible monthly.

Q5. If the nominal rate of discount per annum convertible half-yearly is 4%, find the equivalent:

a) Nominal rate of discount per annum convertible monthly;

b) Nominal rate of interest per annum convertible monthly;

c) Effective rate of interest per annum;

d) Discount factor v.

Q6. The rate of interest per annum convertible quarterly is 9%. Calculate:

a) The equivalent nominal rate of interest per annum convertible monthly;

b) The equivalent nominal rate of discount per annum convertible monthly.

Q7. A loan of £50,000 is repayable in 91 days at a simple rate of interest of 13% per annum. Calculate: The equivalent nominal rate of discount per annum convertible half-yearly.

Q8. The nominal rate of discount per annum convertible monthly is 8.5%. Calculate:

a) The equivalent effective rate of discount per annum.

b) The equivalent rate of interest per annum convertible quarterly.

Q9. An individual invests a lump sum of £5,000 for a period of 30 years at the following rates of interest:-

• Years 1-8: 6% per annum effective.
• Years 9-25: 7% per annum convertible quarterly.
• Years 26-30: 8% per annum convertible every 2 years.

Calculate the accumulated value of the investment after 30 years.

Q10. The force of interest is 5% per annum. What is the equivalent effective rate of interest per annum?

Q11. The effective annual rate of interest i is 5%. What is the constant force of interest, i is δ which would lead to this effective rate of interest, i.e. the equivalent constant force of interest?

Q12. An amount of money accumulates at a constant force of interest equal to 0.086178 per annum.

a) Find the accumulated value of one unit (1) invested for 5 years.

b) Find the accumulated value of £2,000 invested for 5 years.

c) What is the effective rate of interest per annum corresponding to this force of interest?

Q13. The force of interest is 5% per annum. Calculate the equivalent nominal rate of interest per annum convertible quarterly.

Q14. On her 21^st birthday, a woman will receive £5,000 as a result of a deposit made by her grandparents on the day she was born. How much was the deposit if the interest earned is equivalent to a force of interest of 7% per annum?

Q15. The force of interest is 5% per annum. Calculate the following:

a) The equivalent effective rate of discount per annum;

b) The nominal rate of Discount Convertible quarterly.

Q16. An amount of money accumulates at a constant force of interest equal to 9% per annum.

a) What is the effective annual rate of interest corresponding to this force of interest?

b) Find the nominal rate of interest per annum, i^(p) for p = 2 and p = 12.

c) What is the effective annual rate of discount corresponding to this force of interest?

d) Find the nominal rate of discount per annum, d^(p) for p = 2 and p = 12.

Q17. Let time be measured in years. Find the accumulated value after 10 years, of an investment of £500 given that for all t₁ ≤ t₂, A(t₁ ,t₂) = e^{0.04(t_2-t_1)}.

Q18. An amount of £1000 accumulates at a constant force of interest equal to 0.086178 for three years. Find the accumulated value after three years.

Q19. The force of interest δ(t), is a function of time, and at any time t , measured in years is given by the formula:

δ(t) = 0.005t + 0.0002t² for all t

Calculate the accumulated value at time t = 8 of an investment of £1 made at time.

a) t = 0

b) t = 5

Q20. Derive and simplify as far as possible expressions for v(t), where v(t) is the present value of a unit sum of money due at time t, given that the force of interest δ(t), is a function of time and at any time t, measured in years, is given by:

δ(t) = 0.04 + 0.01t, 0 ≤ t < 10

δ(t)= 0.05, t ≥10

Q21. Given that the force of interest is as that described in Question 20 above, calculate the present value of £10,000 due at the end of 15 years.