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30. Future Value of an Annuity Due If the future value of an ordinary, 7-year annuity is
$10,000 and interest rates are 4 percent, what is the future value of the same annuity due?
31. Future Value of an Annuity Due If the future value of an ordinary, 4-year annuity is
$1,000 and interest rates are 6 percent, what is the future value of the same annuity due?
32. Effective Annual Rate A loan is offered with monthly payments and a 10 percent APR.
What is the loan's effective annual rate (EAR)?
33. Effective Annual Rate A loan is offered with monthly payments and a 6.5 percent APR.
What is the loan's effective annual rate (EAR)?
34. Future Value Given a 4 percent interest rate, compute the year 6 future value of deposits
made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,200, and $1,400.
35. Future Value Given a 6 percent interest rate, compute the year 6 future value of deposits
made in years 1, 2, 3, and 4 of $1,200, $1,400, $1,400, and $1,500.
36. Future Value of Multiple Annuities Assume that you contribute $100 per month to a
retirement plan for 20 years. Then you are able to increase the contribution to $200 per month for
another 20 years. Given a 6 percent interest rate, what is the value of your retirement plan after
40 years?
37. Future Value of Multiple Annuities Assume that you contribute $200 per month to a
retirement plan for 15 years. Then you are able to increase the contribution to $400 per month for
another 25 years. Given a 5 percent interest rate, what is the value of your retirement plan after
40 years?
38. Present Value Given a 5 percent interest rate, compute the present value of deposits
made in years 1, 2, 3, and 4 of $1,000, $1,400, $1,400, and $1,500.
39. Present Value Given a 7 percent interest rate, compute the present value of deposits
made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,500, and $1,500.
40. Present Value Given a 4 percent interest rate, compute the present value of deposits
made in years 1, 2, 3, and 4 of $1,000, $1,200, $1,200, and $1,400.
41. Present Value Given a 6 percent interest rate, compute the present value of deposits
made in years 1, 2, 3, and 4 of $1,200, $1,400, $1,400, and $1,500.
42. Present Value of Multiple Annuities A small business owner visits his bank to ask for a
loan. The owner states that he can repay a loan at $1,500 per month for the next three years and
then $500 per month for the two years after that. If the bank is charging customers 5.5 percent
APR, how much would it be willing to lend the business owner?
43. Present Value of Multiple Annuities A small business owner visits his bank to ask for a
loan. The owner states that he can repay a loan at $2,000 per month for the next three years and
then $1,000 per month for the two years after that. If the bank is charging customers 8.5 percent
APR, how much would it be willing to lend the business owner?
44. Present Value of a Perpetuity A perpetuity pays $100 per year and interest rates are 6.5
percent. How much would its value change if interest rates increased to 9 percent?
45. Present Value of a Perpetuity A perpetuity pays $50 per year and interest rates are 9
percent. How much would its value change if interest rates decreased to 6 percent?
46. Future and Present Value of an Annuity Due If you start making $100 monthly
contributions today and continue them for five years, what is their future value if the
compounding rate is 10 percent APR? What is the present value of this annuity?
47. Future and Present Value of an Annuity Due If you start making $25 monthly
contributions today and continue them for four years, what is their future value if the
compounding rate is 6 percent APR? What is the present value of this annuity?
48. Compound Frequency Payday loans are very short-term loans that charge very high
interest rates. You can borrow $500 today and repay $550 in two weeks. What is the compound
annual
rate implied by this 10 percent rate charged for only two weeks?
49. Compound Frequency Payday loans are very short-term loans that charge very high
interest rates. You can borrow $600 today and repay $675 in two weeks. What is the compound
annual
rate implied by this 12.5 percent rate charged for only two weeks?
