An investment of $100 grows in four years to $345. The investor observes that the annual arithmetic rate of return and the geometric rate of return were the same over this period. The annual arithmetic rate of return must be ________.
Answer(s): E
If the annual geometric rate of return is r, then 100 * (1 + r)^4 = 345. This gives r = 36.29%. Note that the only way the mean will be equal to the geometric mean if every year, the stock experienced a return of 36.29% per year.
A sample of the monthly amounts spent for food by families of four receiving food stamps approximates asymmetrical distribution. The sample mean is $150 and the standard deviation is $20. About 95 percent of the monthly food expenditures are between what two amounts?
Answer(s): B
About 95% of the observations lie between plus and minus two standard deviations from the mean.
A manufacturer of headache medicine claims it is 70 percent effective within a few minutes. That is, out of every 100 users 70 get relief within a few minutes. A group of 12 patients are given the medicine. If the claim is true, what is the probability that 8 have relief within a few minutes?
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 = 12, r = 8,p = 0.7 and q = 0.3. Therefore we have 12!(0.7^8)(0.3^4)/8!4! = 0.231.
If you deposit $400 a month, beginning next month, for 10 years into an account paying 8% per year, compounded monthly, how much is in your account after that last deposit?
On the BAII Plus, press 120 N, 8 divide 12 = I/Y, 0 PV, 400 PMT, CPT FV. On the HP12C, press 120 n, 8 ENTER 12 divide i, 0 PV, 400 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.
If you deposit $245 into an account paying 5.5% per year simple interest, how much interest will be earned after 15 months?
The question only asks for the earned interest, not the total amount in the account. On the BAII Plus, press 245 x 0.055 x 15 divide 12 = to see the answer. On the HP12C, press 245 ENTER 0.055 x 15 x 12 divide to see the answer.
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