Question

Question 3 Jack and Sally are saving for next year’s Halloween party (they rightfully cancelled this year’s party). They each have different value of time (monthly interest rates: ijack and isally). There are two saving plans:

1] Put aside $200 now

2] Save $300 after six months.

They both looked at those plans and disagreed on the outcome. Jack prefers plan 1 while Sally prefers plan 2. They went to a common friend to arbitrate who, in turn looked at plans 1 and 2 and said they are equivalent. That is, it does not matter which plan to be selected. The friend has his own value of time: ifriend.

a] What is the value of time of the friend (monthly interest rate of the friend)?

b] Describe who has a higher value of time: Jack or Sally?

c] Who has higher value of time: Jack or the friend? You need to provide clear analysis to these problems not just final answers.

Answer 1

a)

interest rate ifriend gives the same future value for $200 invested now and $300 invested after 6 months.

$200 is invested for 12 months and $300 for 6 months

since both are equivalent

implies, 200X(1+ifriend)¹² = 300X(1+ifriend)⁶ ---------------(1)

(1+ifriend)⁶ = 300/200 = 1.5

1+ifriend = 1.5^(1/6) = 1.069913

ifriend = 1.069913 - 1 = 0.069913 = 6.9913%

b)

For Jack equation 1 would become

200X(1+ijack)¹² > 300X(1+ijack)⁶

implies, (1+ijack)⁶ > 300/200

(1+ijack)⁶ > 1.5

1+ijack > 1.069913

ijack > 6.9913%

For Sally equation 1 would become

200X(1+isally)¹² < 300X(1+isally)⁶

implies, (1+isally)⁶ < 300/200

(1+isally)⁶ < 1.5

1+isally < 1.069913

isally < 6.9913%

implies ijack > isally

Jack has higher value of time than Sally

c)

Using the results above, ijack > ifriend

Jack has higher value of time than friend