These are Theory of Interest questions:
(1) At a nominal annual interest rate of 14% convertible quarterly, how long will it take youto double your money? (Provide an answer in years, to two decimal places.)
(2) If you invest $10,000 now, how much will you have five years from now if your moneygrows at a nominal annual rate of 8% convertible monthly?
(3) On September 1, 2015, you invest $X into an account earning a nominal annual rate of11% convertible semi-annually. On July 1, 2019, your account has grown to $18,467.Find X.
(4) At what constant force of interest will you double your money in 6.5 years?
(5) Let (2) d be the nominal annual rate of discount convertible semiannually at which youcan double your money in 8 years. Find i(4), the equivalent nominal annual rate ofinterest convertible quarterly.
(6) A cash flow of $10,000 forty-two months from now has a present value, now, of $6,390.Find (4) i , the nominal annual rate convertible quarterly that is consistent with thissituation.
(7) Abby offers to pay you $5,000 five years from now. Ben offers to pay you $4,500 attime t. The effective annual interest rate is 10%. Find the value of t such that you areindifferent between Abby's and Ben's offers. (Note: "indifference" means that bothoffers have the same present value.) Express t in years, to two decimal places
(8) You have the following choice in buying a product:Option A: You can pay 12% below the current retail price now.Option B: You can pay 4% below the current retail price two years from now.At what annual effective rate of interest are you indifferent between these two options?(Note: this is a very common type of problem in theory of interest. Interpret"indifference" to mean that the present values (now) of the two options are equal.)
(9) Cash flows of $5,000 at time 1 and $3,000 at time 2 have a total present value at time 0 of$7,000. Find the constant effective annual interest rate i consistent with this situation.(Note: You might find the quadratic formula useful.)
(10) $1,000 is invested for 20 years. For years 1-5, the investment rate is i(2) =11%. Foryears 6-10, the investment rate is δ = 6% . For years 11-15, the investment rate isd(4) =14% . For years 16-20, the investment rate is i = 8% . Find the accumulated valueof the investment at the end of the 20 years.