Annika Scholten bought a 10,000.00, 13-week treasury bill at 5%. What is her effective rate? Round to the nearest hundredth percent. use 360 days and not 365
5.06%
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To find Annika Scholten's effective rate on her 13-week treasury bill, we can use the formula for effective yield:
Effective Rate = (1 + (Nominal Rate / Number of Periods))^(Number of Periods) - 1
In this case, the nominal rate is 5%, and the number of periods is 13 weeks. Since the treasury bill is a 13-week bill, the number of periods is 1.
Plugging in the values, we have:
Effective Rate = (1 + (0.05 / 1))^(1) - 1
= (1 + 0.05)^(1) - 1
= (1.05)^(1) - 1
= 1.05 - 1
= 0.05
Therefore, Annika Scholten's effective rate on her 13-week treasury bill is 0.05, which is equal to 5%.
To calculate the effective rate on a 13-week treasury bill, we need to use the formula for calculating effective rate:
Effective Rate = (1 + (nominal rate / number of compounding periods)) ^(number of compounding periods / number of days) - 1
In this case, the nominal rate is 5%, the number of compounding periods is 4 (since there are 13 weeks in a quarter), and the number of days is 360 (using 360 days for the year instead of 365).
Let's calculate the effective rate step by step:
1. Convert the nominal rate into a decimal: 5% = 5 / 100 = 0.05
2. Calculate the base: 1 + (0.05 / 4) = 1.0125
3. Calculate the exponent: (4/13) * (360/360) = 4/13
4. Calculate the effective rate: 1.0125 ^(4/13) - 1 = 0.015804
5. Round the effective rate to the nearest hundredth percent: 0.015804 = 1.58%
Therefore, the effective rate on Annika Scholten's 10,000.00 13-week treasury bill is approximately 1.58%.