Question

(6 points) On December 8, 2020, Cecilia buys a T-Bill with a face value of $30000 maturing on February 26, 2021. She pays $29400. a) Find Cecilia's annualized yield rate. Answer = | %. b) Find the simple (annual) rate of discount on the T-Bill. Answer = %. c) On January 20, 2021, Cecilia will sell the T-Bill to Delila at a price that provides Delila with a simple (annual) discount rate of 13%. i. How much will Delila pay to Cecilia? Answer = $ ii. Find Cecilia's annualized yield. Answer = %.

Answer 1

a) Cecilia's annualised yield rate

Days for which bill was held = 81 days

Earning for the period = $ 600

Annual yield = $ 600 × 365 ÷ 81

= $ 2704

Annualised yield rate = 2704 ÷ 29400 × 100

= 9.197 %

b) Simple rate of discount

Rate of discount = Annual yield ÷ Maturity Value

= 2704 ÷ 30000 × 100

= 9.013 %

c.i) How much will Delila pay to Cecilia

Discount for the year = 30000 × 13%

= $ 3900

Days left = 38 days

Discount for the period = 3900 × 38 ÷ 365

= $ 406.027

Payment by Delila = 30000 - 406.027

= $ 29593.97

c.ii) Cecilia's annualised yield

Amount Cecilia earned = 29593.97 - 29400

= 193.97

Days for which bill was held = 43 days

Annualised yield = 193.97 × 365 ÷ 43

= $ 1646.49

Annualised yield rate = 1646.49 ÷ 29400 × 100

= 5.60 %

Bimonthly interest rate :

a) Rate = ( [ 1+ (r ÷ m) ] ^ m ) - 1

m = 24 × 6 = 144

r = 0.09

Rate = ( [ 1 + (0.09 ÷ 144) ] ^ 144 ) - 1

= 9.414 %

b) m = 24 × 4 = 96

r = 0.05

Rate = ( [ 1 + (0.05 ÷ 96) ] ^ 96 ) - 1

= 5.126 %

c) m = 24 × 12 = 288

r = 0.04

Rate = ( [ 1 + (0.04 ÷ 288) ] ^ 288 ) - 1

= 4.081 %

Note : There might be minor variations in results due to rounding off.

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