What annual interest rate, compounded quarterly, would cause a series of 20 quarterly deposits of $800 to accumulate to $25,000, if the first deposit is made three months from today?
Answer(s): D
The value returned by the calculator will be the periodic interest rate which must be multiplied by the number of periods per year to have the correct answer. On the BAII Plus, press 20 N, 0 PV, 800 PMT, 25000 +/- FV, CPT I/Y. Then press x 4 = to see the answer. On the HP12C, press 20 n, 0 PV, 800 PMT, 25000 CHS FV, i. Then press 4 x to see the answer. Make sure the BAII Plus has the P/Y value set to 1.
Bert wants to retire a millionaire. If he is 40 years old today and already has $40,000 in the bank, what monthly deposit would he need to make beginning one month from today and continuing until he retires on his 65th birthday, if the money will earn 8% per year, compounded monthly?
Answer(s): E
The total number of deposits will be 300 (25 years x 12 months/year). On the BAII Plus, press 300 N, 8 divide 12 = I/Y, 40000 PV, 1000000 +/- FV, CPT PMT. On the HP12C, press 300 n, 8 ENTER 12 divide i, 40000 PV, 1000000 CHS FV, PMT. Note that the answer will be displayed as a negative number. Make sure the BAII Plus has the P/Y value set to 1.
What annual interest rate, compounded annually, is equivalent to 9% per year, compounded quarterly?
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 4 N, 9 divide 4 = I/Y, 100 PV, 0 PMT, CPT FV. On the HP12C, press 4 n, 9 ENTER 4 divide i, 100 PV, 0 PMT, FV. The number displayed will be 109.30. In other words, after one year, $100 has become $109.30. An interest rate of 9.30%, compounded annually, would cause a $100 deposit to become $109.30 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.
Suppose you have two assets, A and B. A has returns of 10%, 2%, and 15%, with probabilities 40%, 50%, and 10% respectively. B has returns of 5%, 10%, and -20%, with probabilities 40%, 50%, and 10% respectively.What is the return covariance between assets A and B?
First we must find the expected returns for A and B. These are 6.50% and 5.00%, respectively. Second, we find the difference between each observation and the average: (10% - 6.5%), (2% - 6.5%), and (15% - 6.5%) for A, and (5% - 5%), (10% - 5%), and (-20% - 5%) for B. Next, we take the probability weighted cross product of these differences and sum them. So we get 3.5% * 0% * 40% + (-4.5%) * 5% * 50% + 8.5% * (-25%) * 10% = - 32.45%%.
The probability that GNP will expand in the next 12 months is called:
Answer(s): A
An unconditional probability takes the form of P(A), the probability that an event (A) will happen. It is unconditional because it is not conditioned on any other event.
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