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

A perpetuity pays $250 per year and interest rates are 8.5 percent. How much would its value change if interest decreased to 5.5 percent? Did the value increase or decrease?

Chase purchased a $23,000 car three years ago using a 14 percent, 6-year car 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 Chase would need to receive for his car? (Assume monthly payments.)

Assume that you contribute $300 per month to a retirement plan for 25 years. Then you are able to increase the contribution to $500 per month for 20 years. Given a 9 percent interest rate, what is the value of your retirement plan after 45 years?

Your firm needs to buy additional physical therapy equipment that costs $27,000. The equipment manufacturer will give you the equipment now if you will pay $7,000 per year for the next five years. Assume your firm can borrow at a 13 percent interest rate. You need to analyze if your firm should pay the manufacturer the $27,000 now or accept the five-year annuity offer of $7,000. Which of the following statements is correct?

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?

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?

What is the present value of a $250 deposit in year 1 and another $50 deposit at the end of year 6 if interest rates are 10 percent?

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?

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?

If the present value of an ordinary, 8-year annuity is $12,500 and interest rates are 9.1 percent, what is the present value of the same annuity due?

A loan is offered with monthly payments and a 6.5 percent APR. What is the loan's effective annual rate (EAR)?

Isaac realizes that he charged too much on his credit card and has racked up $7,000 in debt. If he can pay $275 each month and the card charges 17.55 percent APR (compounded monthly), how long will it take him to pay off the credit card? How much interest expense will Isaac pay during this time?

When interest rates are lower, borrowers can:

A mortgage broker is offering a 30-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 5 percent APR interest rate. After the second year, the mortgage interest charged increases to 8 percent APR. What is the effective interest rate in the first two years? What is the effective interest rate after the second year?

Due to poor spending habits, Ricky has accumulated $10,000 in credit card debt. He has missed several payments and now the annual interest rate on the card is 18.95 percent! If he pays $175 per month on the card, how long will it take Ricky to pay off the card?

When computing the future value of an annuity, the higher the compound frequency:

A car company is offering a choice of deals. You can receive $2,000 cash back on the purchase, or a 2 percent APR, 3-year loan. The price of the car is $17,000 and you could obtain a 3-year loan from your credit union, at 7 percent APR. Which deal is cheaper?

You just bought a new home and have a 30-year mortgage with monthly payments. Which statement regarding your mortgage is correct?

A small business owner visits his bank to ask for a loan. The owner states that she can repay a loan at $1,500 per month for the next 3 years and then $500 per month for three years after that. If the bank is charging customers 10 percent APR, how much would it be willing to lend the business owner?

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?