How long will it take for an initial deposit of $1,500 to grow to be $4,000, if the interest rate is 5% per year, compounded annually?
Answer(s): B
Either the $1,500 or the $4,000 must be entered as a negative number - it won't matter which. On the BAII Plus, press 5 I/Y, 1500 PV, 0 PMT, 4000 +/- FV, CPT N. On the HP12C, press 5 i, 2500 PV, 0 PMT, 4000 CHS FV,F. Note that the HP12C will indicate 21 years for the answer. Make sure the BAII Plus has the P/Y value set to 1.
Ball-Bearing, Inc. produces ball bearings automatically on a Kronar BBX machine. For one of the ball bearings, the mean diameter is set at 20mm. the standard deviation of the production over a long period of time was computer to be 0.150 mm. What percent of the ball bearings will have a diameter of 20.27 mm or more?
Answer(s): E
z = (x-u)/sigma = 20.27 - 20/0.15 = 1.8. from the z-table, z = 1.8 is 0.4641. So 1.0 - 0.9641 = 0.0359.
In an investment environment, an initial outlay of $100 grows to $156 in 7 years. The quarterly compounded rate of annual interest implicit in this is:
There are 28 quarters in 7 years. If the quarterly compounded rate is r, then we have 100*(1+r/4)^28 = 156, giving r = 6.4%
David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period twenty-five customers buy gasoline at this station. What is the probability that at least ten pay in cash?
This is a binomial distribution: n!(p^r)(q^(n-r))/r!(n-r)!. n = 25, r = 10, p = 0.4 q = 0.6 P(10) = 25!(0.4^10)(0.6^15)/10!15! = 0.1612P(11) = 25!(0.4^11)(0.6^14)/11!14! = 0.1465P(12) = 25!(0.4^12)(0.6^13)/12!13! = 0.1140P(13) = 25!(0.4^13)(0.6^12)/13!12! = 0.0760P(14) = 25!(0.4^14)(0.6^11)/14!11! = 0.0434P(15) = 25!(0.4^15)(0.6^10)/15!10! = 0.0212P(16) = 25!(0.4^16)(0.6^9)/16!9! = 0.0088P(17) = 25!(0.4^17)(0.6^8)/17!8! = 0.0031Summing up we get close to 0.574.We can continue until r = 25 but the probability gets smaller and converges to 0.575.
Consider the following three investments:Future valueyearsinterest rate1.$50,000 89% per year2.$20,000 612% per year3.$35,000 37% per yearThe present values of the 3 investments are:
Answer(s): C
Future value = Present value*(1+r)^N for annual compounding. Therefore, Future valueyearsratePresent Value1.50,000 89% 50,000/(1.09)^8 = 25,0932.20,000 612% 20,000/(1.12)^6 = 10,1333.35,000 37% 35,000/(1.07)^3 = 28,570Note that the future value must always be greater than the present value.
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