1) An admissions test given by a university contains 10 true-false questions. Eight or more of the questions must be answered correctly in order to be admitted.
a) How many different ways can the answer sheet be filled out?
b) How many different ways can the answer sheet be filled out so that 8 or more questions are answered correctly?
2) Choosing a Car Loan
A car dealer offers Mike the choice of two loans:
a) $3000 for 3 years at 12% per annum simple interest
b) $3000 for 3 years at 10% per annum compounded monthly
Which loan costs Mike the least?
3) Depletion Problem
How much should Mr. Graff pay for a gold mine expected to yield an annual return of $20,000 and to have a life expectancy of 20 years, if he wants to have a 15% annual return on his investment and he can set up a sinking fund that earns 10% a year?
4) Trust Fund Payouts
John is the beneficiary of a trust fund set up for him by his grandparents. If the trust fund amounts to $20,000 earning 8% compounded semiannually and he is to receive the money in equal semiannual installments for the next 15 years, how much will he receive each 6 months?
5) Buying a Car
A student borrowed $4000 from a credit union toward purchasing a car. The interest rate on such a loan is 14% compounded quarterly, with payments due every quarter. The student wants to pay off the loan in 4 years. Find the quarterly payment.
Let C(n,m)=n!/(m!(n-m)!) is the number of choices to select m items from n items.
(a) Each question has two answers T or F. We have totally 10 questions. Thus the number of different ways to fill out the sheet is: 2^10=1024
(b) 8 or more questions are answered correctly. It means we select 8 or 9 or 10 questions out of 10 questions. Those selected questions are answered correctly and those not selected are answered incorrectly. The number of different ways to fill out the sheet is:
(a) For simple interest, the final cost ...
Problems involving combinations, interest, annuities and loans are answered with calculations shown.