Question

A T-bill of face value $100 matures on January 1, 1995, at a simple discount of 6% per year. • Find the present value on July 1, 1994. • Find the value of i equivalent to d.

Answer 1

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Answer (1):

a.

Given:

Time between July 1, 1994 to January 1,1995 = n = 6 months = 0.5 year

Discount % (d) = 6%

PV can be calculated as FV (1-d)^0.5

=> PV at July 1, 1994 = 100(0.94)^0.5

=> PV = $ 96.95

b.

We know the relationship between i and d as

i = d/(1-d)

=> i = 0.06/0.94

=> i = 0.0638 = 6.4%

Answer (2):

Let us assume that P is the purchase price by the customer.

First condition:

By given that 90% has to be paid within two months of sale:

=> 0.9 P to be paid in ( 2/12 = ) 1/6 of a year

PV of that payment = 0.9P (1 + 0.08 )^-1/6  

where r is the rate = 8% and the formula used is PV = C.F (1+r)^-n

Second condition:

Deduct X% now and pay the rest

=> Paying P - (X/100)*P

Equating first and second conditions

=>P - (X/100)*P = 0.9P (1.08 )^-1/6  

=> (1-X/100) = 0.9*(1.08)^-1/6  

=> (1-X/100)(1.08)^1/6   = 0.9