Question

2. Consider the following sequences of end of year returns: i). 20, 15, 10, 10, 5 ii). 20, 15, 15, 5, 5 Which sequence is preferable if the interest rate, compounded annually, is 4%?

Consider the following sequences:

i) 20, 15, 10, 10, 5

ii) 20, 15, 15, 5, 5

Which sequence is preferable if the interest rate, compounded annually, is 4%

Answer 1

I will calculate present value of these return. Whose present value will be higher that sequence will be better.

i) 20, 15, 10, 10, 5

5 15 15 10 20 10 10 + 1 i 10 + + + + (1 i)2 (1 i)3 (1+ i)4 (1+ i)5 5 1.04 (1.04)(1.04)3 54.65 (1.04)4 (1.04)5 20

ii) 20, 15, 15, 5, 5

15 5 5 15 15 20 15 + (1 i)2 (1 i)3 (1+ i)4 (1+ i)5 + + + 1.04(1.04)(1.04)3 + 1 i 5 54.81 (1.04)4 (1.04)5 20

So sequence 2 nd is better