Assignment:
The Treasury Department
The Treasury Department auctioned $21 billion in three-month bills in denominations of ten thousand dollars at a discount rate of 4.965%.
What would be the effective rate of interest? Round your answer to the nearest hundredth percent.Answer :-
To figure out the amount you pay,
first change the yearly discount rate to quarterly
(divide by 4... because 3 months is ¼ of a year)
0.04965/4 (1- 0.04965/4)
=0.9875875
the amount you pay for $1 multiply by the face value of the bill
10,000*0.9875875
= 9,875.875
To find the effective interest rate, find the amount of interest = 10000-9,875.875 and divide the interest by
9,875.875 (10000-9,875.875)/9,875.875
= 0.0125685065880238
Multiply by 4 to get the effective yearly rate 0.0125685065880238*4
= 0.0502740263520952 in percent,
That is 5.0274 % rounded to the nearest hundredth we get 5.03%