The Investment Company Institute reported in its Mutual Fund Fact Book that the number of mutual funds increased from 410 in 1985 to 857 in 1995. What is the geometric mean annual percent increase in the number of funds?
Answer(s): E
There are 11 years involved. The geometric mean = [(1 + 857/410)^1/10]-1. In words, it is the 10th square root of (1 + 857/410) minus 1. So we have GM = (1 + 2.09)^(1/10) - 1 = 0.0765 = 7.65%
You are faced with a counting problem in which you must choose k objects from n total objects. The order of choosing matters. The counting method you should use is:
Answer(s): D
We need the general permutation formula, which gives the number of ways that k objects can be chosen from n items, with regard to order. The formula is n_P_k = n! / (n-k)!
How much would an original deposit of $2,500 grow to be after 6 and a half years, if the deposit earns interest at 8.5% per year, compounded monthly?
Answer(s): A
On the BAII Plus, press 2500 PV, 0 PMT, 78 N, 8.5 divided by 12 = I/Y, then press CPT FV. On the HP12C, press 2500 PV, 0 PMT, 78 n, 8.5 ENTER 12 divide i, then press FV. The answer will be displayed as a negative number. Make sure that the BAII Plus has the P/Y value set to 1.
If you buy an item and pay for it with 60 monthly payments of $75 that begin next month, what was the cash price today, if interest accrues at 11% per year, compounded monthly?
The cash price would be the present value of the payments made using the specified interest rate. On the BAII Plus, press 60 N, 11 divide 12 = I/Y, 75 PMT, 0 FV, CPT PV. On the HP12C, press 60 n, 11 ENTER 12 divide i, 75 PMT, 0 FV, PV. Note that the answer will be shown as a negative number. Make sure the BAII Plus has the P/Y value set to 1.
Suppose that stocks A, B, C, and D are independent with respect to their price movement, and have probabilities of increasing of 0.25, 0.50, 0.40, and 0.30. What is the probability that stocks A and C will increase in price, while stocks B and D fail to increase?
Answer(s): C
If events are independent, then the joint probability of them occurring together is just the product of the individual probabilities. So P(AC) = 0.25 * 0.40 = 10%. To this, we multiply the probabilities of B and D failing to increase: 10% * (1 - 0.50)*(1 - 0.30) = 3.5%.
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