What annual interest rate, compounded annually, is equivalent to 6% per year, compounded monthly?
Answer(s): B
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 12 N, 6 divide 12 = I/Y, 100 PV, 0 PMT, CPT FV. On the HP12C, press 12 n, 6 ENTER 12 divide i, 100 PV, 0 PMT, FV. The number displayed will be 106.17. In other words, after one year, $100 has become $106.17. An interest rate of 6.17%, compounded annually, would cause a $100 deposit to become $106.17 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.
What is the Net Present Value of this series of annual cash flows: Year 0: <$20,000>, Year 1: $15,000, Year 2:$5,000, Year 3: $7,500, using an interest rate of 10% per year? (Note that the <> are used to indicate a negative number).
Answer(s): E
On the BAII Plus, press CF 2nd CLRWork 20000 +/- ENTER DownArrow 15000 ENTER DownArrow DownArrow 5000 ENTER DownArrow DownArrow 7500 ENTER DownArrow DownArrow 2nd Quit. Then press NPV 10 ENTER DownArrow CPT. On the HP12C, press these keys: 20000 CHS BlueShift CFo 15000 BlueShift CFj 5000 BlueShift CFj 7500 BlueShift CFj Then press 10 i, YellowShift NPV. The "DownArrow" represents the downward-pointing arrow on the top row of the BAII Plus keyboard.
Three young children approach a gum ball machine, each with a nickel to spend. The machine has just been filled with 50 black, 150 white, 100 red and 100 yellow balls that have been thoroughly mixed. Sue and Jim approached the machine first. They both said they wanted red gum balls. What is the likelihood they both will get their wish?
100/400*99/399 = 0.062
Which of the following is not a characteristic of the normal probability distribution?
Answer(s): D
The normal probability distribution is not skewed but bell shaped and symmetric.
In a regression, the independent variable explains 79% of the variance in the dependent variable, leaving 21% unexplained. The slope coefficient is 0.67 and the intercept equals -10.2 The correlation coefficient between the two variables is
In a univariate regression, the correlation coefficient between the dependent and the independent variables equals the square root of R-square. However, you should also be careful about the sign, which is not given by the R-square. Rather, you have to look at the sign of the slope coefficient. In this case, the slope coefficient is positive, implying that the dependent and the independent variables are positively correlated. The R-square equals 79% so the correlation coefficient equals +sqrt(0.79) = 0.89.
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