CFA Exam Question of the Day

Level I | Level II | Level III

2023-03-26

Question:
A manufacturer of headache medicine claims it is 70 percent effective within a few minutes. That is, out of every 100 users 70 get relief within a few minutes. A group of 12 patients are given the medicine.

If the claim is true, what is the probability that 8 patients have relief within a few minutes?

Select an Answer:
0.168
0.001
0.231
0.667
Rationale:
This is a binomial probability. The probability of getting r successes out of n trials where the probability for success of each trial is p and the probability for failure of each trial is q (where q = 1 − p) is given by:



Here, n = 12, r = 8, p = 0.7 and q = 0.3. Therefore, we have:


2023-03-25

Question:
An intern with Churn Brothers Brokerage has been instructed to calculate the coupon rate on an inverse floater. Assume the following information:
  • Reference rate = LIBOR = 6.75% per year
  • K = 12% per year
  • L = 35%
Using this information, what is the current annual coupon rate on this inverse floater?

Select an Answer:
34.19%
10.95%
9.64%
14.36%
Rationale:
The equation used to determine the coupon rate on an inverse floater is as follows:

Coupon rate = K − L × Reference rate

In this example, all the necessary information has been provided, and the calculation of the coupon rate is as follows:

Coupon rate = 12% − 0.35(6.75%) = 9.638%

Inverse floaters are debt instruments which have a coupon rate that moves inversely with a quoted reference rate, i.e., as the reference rate X increases, the coupon rate on an inverse floater tied to X would decrease.

2023-03-24

Question:
David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one hour period twenty-five customers buy gasoline at this station.

What is the probability that more than ten and less than fifteen customers pay in cash?

Select an Answer:
.380
.562
.401
.541
Rationale:
Binomial distribution:



n = 25, r = 10, p = 0.4, q = 0.6



Summing up: 0.3799

2023-03-23

Question:
A bank savings account offers a savings rate of 3.5% per year, compounded annually.

How long would it take for an investment of $710 to grow to $1,000?

Select an Answer:
8 years
10 years
11 years
9 years
Rationale:
If it takes n years for the growth, then:

1,000 = 710(1 + 3.5%)n

Solving for n gives 9.96 years.

2023-03-22

Question:
An insurance agent has appointments with four prospective clients tomorrow. From past experience the agent knows that the probability of making a sale on any appointment is 1 out of 5.

Using the rules of probability, what is the likelihood that the agent will sell a policy to 3 of the 4 prospective clients?

Select an Answer:
0.410
0.250
0.500
0.026
Rationale:
This is a binomial probability. The probability of getting r successes out of n trials where the probability of success for each trial is p and the probability of failure for each trial is q (where q = 1 − p) is given by:



Here n = 4, r = 3, p = 0.20, and q = 0.80. Therefore, we have: