Tiffany purchased a $10,000, 13-week Treasury bill that's paying 2.25%. What is the effective rate on this T-bill?
A. 2.26%
B. 2.2%
C. 2.0%
D. 2.7%
Tiffany purchased a $10,000, 13-week Treasury bill that's paying 2.25%. What is the effective rate on this T-bill?
Answer: 2.26%
Because T-bill is a simple discount note we will use a formula for simple interest I=P x r x t (I is Interest, r is rate in decim., t is time)
I=? P= 10000 r= 0.0225( 2.25% : 2.25/100% = 0.0225)
t=0.25 (13 weeks/52 weeks)
I= 10000 x 0.0225 x 0.25=$ 56.25 ( discount)
Because T-bill is a simple discount note:
$10000 - $56.25 =$9943.75
Next: I=Prt r=I/Pt r=? P=9943.75 t=0.25 (13 weeks/52 weeks)
r= $56.25/($9943.75 x 0.25)= 56.25/2485.9375=0.022627 (or 2.26%)
I = Po*r*t = 10,000*(0.0225/52)*13 =
56.25 = Int. for 13 weeks.
(56.25/13) * 52 = $225 = Int./yr.
%I = (225/10,000)*100% = 2.25%
J. Ryan discounts an 80-day note for $15,000 at 12%. The bank discount is (assume ordinary interest):
$14,600
$15,400
$400
$15,000
None of these
for sure it is not B) 2.2 i got this wrong
To calculate the effective rate on a Treasury bill, we need to consider the discount rate and the length of time the bill is held for.
In this case, we have a 13-week Treasury bill that is paying 2.25%. Since Treasury bills are sold at a discount, we need to calculate the discount rate first.
The discount rate can be calculated using the formula:
Discount rate = (Face Value - Purchase Price) / Face Value
In this case, the face value is $10,000 and the purchase price is not provided. So, to calculate the discount rate, we need to know the purchase price of the bill.
Once we have the discount rate, we can calculate the effective rate using the formula:
Effective rate = (1 + Discount rate)^(52/13) - 1
The exponent (52/13) represents the number of 13-week periods in a year.
Since we don't have the purchase price, we can't calculate the exact effective rate in this case. Therefore, it is not possible to determine the correct answer from the options provided (A, B, C, D).