Question

I am getting confused with this chapter about notes and bank discounts, does anyone know about this? Thanks
The Treasury Department auctioned $21 billion in 3-month bills in denominations of $10,000 at a discount rate of 4.965%. What would be the effective rate of interest? Round your answer to the nearest hundredth percent.

Answer 1

I think you pay less than face value for the 3-month bill.
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%