What annual interest rate, compounded annually, is equivalent to 8% per year, compounded semiannually?
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 theending FV to the beginning PV will indicate the annual rate earned. On the BAII Plus, press 2 N, 8 divide 2 = I/Y, 100 PV, 0 PMT, CPT FV. On the HP12C, press 2 n, 8 ENTER 2 divide i, 100 PV, 0 PMT, FV. The number displayed will be 108.16. In other words, after one year, $100 has become $108.16. An interest rate of 8.16%, compounded annually, would cause a $100 deposit to become $108.16 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.
An insurance agent has appointments with four prospective clients tomorrow. From past experience the agent knows that the probability of making a sale on any appointment is 1 out of 5. Using the rules of probability, what is the likelihood that the agent will sell a policy to 3 of the 4 prospective clients?
Answer(s): D
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)!.Here n = 4, r = 3,p = 0.20 and q = 0.80. Therefore we have 4!(0.2^3)(0.8^1)/3!1! = 0.026.
An investor has a quarterly compounded required rate of return of 9% per year. How much will he pay for a nine-year ordinary annuity that pays $100 per year?
Answer(s): C
The annually compounded rate equals (1 + 9%/4)^4 - 1 = 9.3%. Therefore, the present value of the annuity equals 100/0.093*[1 - 1/1.093^9] = $592.6.
A relative frequency distribution is
Answer(s): A
A relative frequency distribution is an aggregation of raw data in the form of a probability distribution, a collection of relative frequency classes with the relative frequencies, and a grouping of data into nonoverlapping categories.
Suppose the probability that electricity prices will rise any given quarter is 0.60, and the probability that oil prices will stay level or decline is 0.40. If electricity prices rise, corporate profits will decline by 2% with 90% probability, and increase by 0.5% with 10% probability. If electricity prices decline or stay level, corporate profits will increase 3% with a 65% probability and decline 0.5% with a 35% probability. What is the expected change in corporate profits in the next quarter?
We need the total probability rule for expected value, for which the formula is E(X) = E(X | S_1) * P(S_1) + E(X | S_2) * P(S_2) + ... + E(X |S_n) * P(S_n). Here, E(X) is the expected change in corporate profits. S_1 is the event that electricity prices rise, and S_2 is the event that electricity prices fall. Therefore, E(X) = 0.60 * (-2% *90% + 0.5%*10%) + 0.40 * (3%*65% - 0.5%*35%)= -0.34%, a decline.
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