Suppose you are modeling long-term interest rates, and you believe that supply of corporate debt is a major contributing factor. Suppose you believe that the probability that rates will rise if supply of corporate debt rises is 60%; if the supply of corporate debt stays constant, you believe that there is a 35% chance of increasing interest rates; if the supply of corporate debt falls, you believe that there is a 5% chance of rates increasing. You think that the likelihood of corporate debt increasing is 50%; of staying the same is 40%; of dropping is 10%. What is the unconditional probability of interest rates rising?
Answer(s): C
We use the total probability rule: P(A), the unconditional probability, = P(A|S_1)*P(S_1) + P(A|S_2) *P(S_3) + P (A|S_3) *P(S_3), where the S_i represent mutually exclusive and exhaustive events. So the likelihood of interest rates increasing is 0.60 * 0.50 + 0.35 * 0.40 + 0.05 * 0.10 = 0.30 + 0.14 + 0.005 = 0.445.
If you deposit $1,111 a year, beginning next year, for 20 years into an account paying 7% per year, compounded annually, how much is in your account after that last deposit?
On the BAII Plus, press 20 N, 7 I/Y, 0 PV, 1111 PMT, CPT FV. On the HP12C, press 20 n, 7 i, 0 PV, 1111 PMT, FV. On the BAII Plus, make sure the value of P/Y is set to 1. Note that the answer is displayed as a negative number.
The standard normal probability distribution is one which has:
Answer(s): B
The standard normal probability distribution has a mean of 0 and std. deviation of 1.
A statistician has framed his hypothesis testing problem as:Ho: mean = 100 H1: mean < 100Specify the region for the p-statistic which will lead to the rejection of the null at the 80% significance level.
Answer(s): A
Since the alternative is directional and to the left, we use a left-tailed test. For this, the critical value at 80% level is -0.84. -0.84 is the value above which 80% of the probability mass of the standard normal distribution lies).The rejection region is then given by z-statistic < -0.84.
If you deposit $400 today into an account paying 8% per year, compounded quarterly, how much will be in the account after 42 months?
Answer(s): E
There are 14 quarters in 42 months (42 divide 3 =). On the BAII Plus, press 14 N, 8 divide 4 = I/Y, 400 PV, 0 PMT, CPT FV. On the HP12C, press 14 n, 8 ENTER 4 divide i, 400 PV, 0 PMT, FV. Note that the answer will be displayed as a negative number. Make sure the BAII Plus has the value of P/Y set to 1.
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