Question

Problem 7: Betty and Bob pay $9500 for a $10,000 9-month T-Bill from the country of Freedonia. a. Algebraically find the associated per annum simple discount rate and the per annum simple interest rate.

Answer 1

the concept and calculation is based on the simple interest ,

Amount = principle + Simple interest

=> A = P + PRT = P(1+RT)

Answer A) A= $ 10,000 , P= $ 9500 , T= 9 month = 9/12= 0.75 year

discount rate (R) = (A-P) /PT = (10000-9500) /(9500*0.75) = 7.02%

Answer B) for Bartha , R= 6% = 6/2 = 3% for remaining 6 months , T= 6 months = 6/12=0.5 year

P= A/(1+RT) = 10000/(1+0.03*0.5) = $ 9852.22

Answer C) Return for Betty and Bob ,A= 9852.22 , P=9500 , T=3 months =3/12=0.25 years

R = (A-P) /PT = (9852.22-9500) /(9500*0.25) = 14.83%