A portfolio consists of a six-year annuity paying $250 a year and a perpetuity that pays $300 a year. The payments start at the end of the year. With a discount rate of 9% per year, the portfolio is worth:
Answer(s): C
The value of the perpetuity is 300/0.09 = 3,333. The annuity is worth (250/0.09)*(1-1/(1.09^6)) = 1,121 The portfolio is thus worth 1,121 + 3,333 = 4,454
If all the plots on a scatter diagram lie on a straight line, what is the standard error of estimate?
The standard error of estimate basically measures the difference between the points and the straight line.
You wish to rank n different securities according to the deviation of the market price from your estimate of their intrinsic value. You are curious how many different ways this can come out. The counting method you should use is:
Answer(s): D
The factorial method allows you to determine the number of ways of arranging n things. Initially, there are n choices for the first item, then n-1 for the second, and so on. The number of combinations is therefore n! = n * (n-1) * (n-2) * (n-3) * ... * (1).
What annual interest rate, compounded annually, is equivalent to 7% per year, compounded semiannually?
Questions of this type are illustrating the concept of an Effective Interest Rate, which is a rate compounded annually that has the same effect as a rate compounded more often than one time a year. As such, a depositor or a creditor is indifferent between them, since they have the same effect. To solve this question, make any deposit and see how much is in the account after one year. The ratio of the ending FV to the beginning PV will indicate the annual rate earned. On the BAII Plus, press 2 N, 7 divide 2 = I/Y, 100 PV, 0 PMT, CPT FV. On the HP12C, press 2 n, 7 ENTER 2 divide i, 100 PV, 0 PMT, FV. The number displayed will be 107.12. In other words, after one year, $100 has become $107.12. An interest rate of 7.12%, compounded annually, would cause a $100 deposit to become $107.12 in one year. Choosing an initial deposit of $100 helps a great deal in these situations. Make sure the BAII Plus has the value of P/Y set to 1.
A random variable, X, has a mean of 12 and a standard deviation of 14. If another variable, Y, is defined by Y = 2X - 3, the coefficient of variation of Y is ________.
Answer(s): B
You should remember two important points:1. Multiplying a random variable by a constant multiplies its mean and standard deviation by the same constant.2. Adding a constant to a random variable increases the mean by the same constant but leaves the standard deviation unchanged.Using these two rules, the mean of Y equals 2 * 12 - 3 = 21. The standard deviation of Y equals 2 * 14 = 28.The coefficient of variation equals the ratio of the standard deviation to the mean. Thus, the coefficient of variation of Y equals 28 / 21 = 1.33.
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