Which security offers a higher effective annual yield?
a) a three month bill selling at $9764
b) a six month bill selling at $ 9539
And calculate the bank discount yield on each bill.
To determine which security offers a higher effective annual yield, we need to calculate the effective annual yield for each option and compare the results.
The formula to calculate the effective annual yield is:
Effective Annual Yield = (1 + Bank Discount Yield / (1 - Bank Discount Yield) * (365 / Days to Maturity)
Now let's calculate the effective annual yield for each option:
For option a) the three-month bill selling at $9764:
Bank Discount Yield = (Face Value - Selling Price) / Face Value
= (10000 - 9764) / 10000
≈ 0.0236
Effective Annual Yield = (1 + 0.0236 / (1 - 0.0236) * (365 / 90)
= (1 + 0.0236 / 0.9764) * 4.0556
≈ 0.0972 or 9.72%
For option b) the six-month bill selling at $9539:
Bank Discount Yield = (Face Value - Selling Price) / Face Value
= (10000 - 9539) / 10000
≈ 0.0461
Effective Annual Yield = (1 + 0.0461 / (1 - 0.0461) * (365 / 180)
= (1 + 0.0461 / 0.9539) * 2.0278
≈ 0.0892 or 8.92%
Therefore, the security with a higher effective annual yield is option a) - the three-month bill selling at $9764, with an effective annual yield of approximately 9.72%.
Now, let's calculate the bank discount yield for each option:
For option a) the three-month bill selling at $9764:
Bank Discount Yield = (Face Value - Selling Price) / Face Value
= (10000 - 9764) / 10000
≈ 0.0236 or 2.36%
For option b) the six-month bill selling at $9539:
Bank Discount Yield = (Face Value - Selling Price) / Face Value
= (10000 - 9539) / 10000
≈ 0.0461 or 4.61%
So, the bank discount yield on the three-month bill is approximately 2.36% and on the six-month bill is approximately 4.61%.