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Free CFA-Level-I Exam Braindumps (page: 189)

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PDF with 3963 Questions

The semiannually compounded rate is 6% quoted on an annualized basis. The equivalent quarterly compounded rate is:

  1. 6.12%
  2. 5.91%
  3. 5.96%
  4. 5.76%

Answer(s): C

Explanation:

To solve such problems, think about investing a dollar for 1 year. The final amount should be the same under both the quotations. Under quarterly compounded rate, r, $1 grows to (1+r/4)^4 in 1 year. Under semiannual compounding, it grows to (1+0.06/2)^2 = 1.0609. Since these two should be equal, we get (1+r/4)^4 = 1.0609, giving r = 5.96%. Note that the quarterly compounded rate must be smaller than the semiannually compounded rate, ruling out 6.12 automatically.



A mortgage holding company has found that 1% of its mortgage holders default on their mortgage and lose the property. Furthermore, 90% of those who default are late on at least two monthly payments over the life of their mortgage as compared to 45% of those who do not default. What is the probability that a mortgagee with two or more late monthly payments will default on the mortgage and lose the property?

  1. None of these answers
  2. 0.019
  3. 0.009
  4. 0.020
  5. 0.018

Answer(s): D

Explanation:

We have P(def) = 0.01. P(not def) = 0.99. P(two late payments/def) = 0.90. P(two late payments/not def) = 0.45. Using Bayes formula: p(def/two late payments) = (0.01*0.9)/(0.01*0.9 + 0.99*0.45) = 0.0198 = 0.020.



During the past six months, the purchasing agent bought:

Tons of Coal 1,200 3,000 500
Price Per Ton $28.50 $87.25 $88.00

What is the weighted mean price per ton?

  1. $89.18
  2. $68.47
  3. None of these answers
  4. $87.25
  5. $72.33

Answer(s): E

Explanation:

(1200*28.5)+(3000*87.25)+(500*88) = 339950. Mean = 339950/4700 = 72.33



Sixty percent of the customers of a fast food chain order the Whopper, fries and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?

  1. 0.186
  2. None of these answers
  3. 1,000
  4. 0.403
  5. 0.000

Answer(s): D

Explanation:

This is a binomial probability. The probability of getting r successes out of n trials where the probability of success each trial is p and probability of failure each trial is q (where q = 1-p) is given by: n!(p^r)[q^(n-r)]/r!(n-r)!.
Therefore, we need to find out the probability of getting 10, 11,12,13,14,15 successes and add them up. Here n=15, p=0.6 and q=0.4. r changes from 10 to 15.
P(10 successes) = 15!(0.6^10)(0.4^5)/10!(15-10)! = 0.1859
P(11 successes) = 15!(0.6^11)(0.4^4)/11!(15-11)! = 0.1268
P(12 successes) = 15!(0.6^12)(0.4^3)/12!(15-12)! = 0.0634
P(13 successes) = 15!(0.6^13)(0.4^2)/13!(15-13)! = 0.0219
P(14 successes) = 15!(0.6^14)(0.4^1)/14!(15-14)! = 0.0047
P(15 successes) = 15!(0.6^15)(0.4^0)/15!(15-15)! = 0.00047
The sum of all the probabilities is 0.403.






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