Question

a. Explain what an annuity is, and distinguish between an annuity due and an ordinary annuity. (3 + 3½ +3½ = 10 marks)

b. An investment of N$120,000 is made for three years at 20% per annum. Calculate the future value or the terminal value of the investment. (5 marks)

c. What is the value of an amount of N$100,000 invested annually for 5 years at an interest rate of 20% per annum? (5 marks)

d. FNB Namibia advertises that investors can become millionaires in 20 years given a rate of interest of 20% compounded annually. What is the annual investment that an investor should make to reach the objective of becoming a millionaire? (10 marks)

e. An investment will result in a receipt of N$80,000 two years from now. The applicable discount rate is 20% per annum. Calculate the present value of the N$80,000 or the amount that an investor would be prepared to invest in order to receive the N$80,000. (10 marks)

Answer 1

a. Annuity : It is the fixed some of money payable at every year on some fixed date.In other words, it is a some of money or investment that is payable at fixed intervals

The only difference between annuity due and ordinary annuity(annuity regular) is as follows :

The annuity for which payments /investments made at the end of every year are called ordinary annuity(annuity regular).

The annuity for which payments /investments made in adavnce are called annuity due.

b. An investment of N$120,000 is made for three years at 20% per annum.

Future or Terminal Value of investment :

=N$120,000*Future Value factor @20% for 3 years

=N$120,000*1.728

=N$207,360

Future or Terminal Value of investment is N$207,360

c.The value of an amount of N$100,000 invested annually for 5 years at an interest rate of 20% per annum

Future value of this investment :

=N$100,000*Annuity Future Value factor @20% for 5 years

=N$100,000*7.442

=N$744,200

Future Value of investment is N$744,200

d.FNB Namibia advertises that investors can become millionaires in 20 years given a rate of interest of 20% compounded annully

Annual investment to be made for becoming millionarire .i.e N$1,000,000

Future value of annual investment @20% for 20 Years =N$1,000,000

Annual Investment*Annuity Future Value factor @20% for 20 years=N$1,000,000

Annual Investment*186.69=N$1,000,000

Annual Investment =N$1,000,00/186.688=N$5,356.53

Annual investment of N$5,356.53 to be made for becoming millionarire

e.An investment will result in a receipt of N$80,000 two years from now. The applicable discount rate is 20% per annum

The present value of the N$80,000 :

N$80,000= Intitial investment*(1+0.2)*(1+0.2)

N$80,000= Intitial investment*1.44

Initial investment=N$80,000/1.44

Initial investment=N$55,555

The present value of the N$80,000 is N$55,555