Exam 5: Time Value of Money 2: Analyzing Annuity Cash Flows

Phoebe realizes that she has charged too much on her credit card and has racked up $10,000 in debt. If she can pay $300 each month and the card charges 18 percent APR (compounded monthly), how long will it take her to pay off the debt?

Your firm needs to buy additional physical therapy equipment that costs $35,000. The equipment manufacturer will give you the equipment now if you will pay $8,000 per year for the next five years. Assume your firm can borrow at a 3 percent interest rate. You need to analyze if your firm should pay the manufacturer the $35,000 now or accept the five-year annuity offer of $8,000. Which of the following statements is correct?

If the present value of an ordinary, 4-year annuity is $1,000 and interest rates are 6 percent, what is the present value of the same annuity due?

What is the interest rate of a 4-year, annual $1,000 annuity with present value of $3,500?

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?

Many people who want to start investing for their future want to start today, which implies an annuity stream that is paid at the beginning of the period. Beginning-of-period cash flows are referred to as

Hank purchased a $20,000 car two years ago using an 8 percent, 5-year loan. He has decided that he would sell the car now, if he could get a price that would pay off the balance of his loan. What is the minimum price Hank would need to receive for his car?

Paige has decided that she wants to build enough retirement wealth that, if invested at 5 percent per year, will provide her with $2,500 monthly income for 20 years. To date, she has saved nothing, but she still has 40 years until she retires. How much money does she need to contribute per month to reach her goal?

What is the present value of a $300 annuity payment over 5 years if interest rates are 8 percent?

Your current $155,000 mortgage calls for monthly payments over 25 years at an annual interest rate of 6 percent. If you pay an additional $50 each month beginning with the first payment, how much interest expense do you save by pre-paying?

You have secured a loan from your bank for two years to build your home. The terms of the loan are that you will borrow $120,000 now and an additional $52,000 in one year. Interest of 9 percent APR will be charged on the balance monthly. Since no payments will be made during the 2-year loan, the balance will grow. At the end of the two years, the balance will be converted to a traditional 30-year mortgage at a 6.5 percent interest rate. What will you pay as monthly mortgage payments (principal and interest only)?

As a college student, you probably receive many credit card offers in the mail. Consider these two offers. The first card charges a 17 percent APR. An examination of the footnotes reveals that this card compounds monthly. The second credit card charges 16.25 percent APR and compounds weekly. What is the effective annual rate of the cheaper card?

If the present value of an ordinary, 10-year annuity is $25,000 and interest rates are 7 percent, what is the present value of the same annuity due?

An annuity due:

Which of the following statements is correct?

If you start making $115 monthly contributions today and continue them for six years, what is their present value if the compounding rate is 12 percent APR? What is the present value of this annuity?

What is the present value, when interest rates are 6.5 percent, of a $100 payment made every year forever?

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?

A local furniture store is advertising a deal in which you buy a $3,500 living room set with three years before you need to make payments (no interest is incurred). How much money would you have to deposit now in a savings account earning 3.5 percent APR, compounded monthly, to pay the $3,500 bill in three years?

Payday loans are very short-term loans that charge very high interest rates. You can borrow $500 today and repay $550 in ten weeks. What is the compound annual rate implied by this 10 percent rate charged for only ten weeks?