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

Payday loans are very short-term loans that charge very high interest rates. You can borrow $200 today and repay $250 in two weeks. What is the compound annual rate implied by this 25 percent rate charged for only two weeks?

What is the future value of a $1,000 annuity payment over 4 years if the interest rates are 8 percent?

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

Joey realizes that he has charged too much on his credit card and has racked up $4,000 in debt. If he can pay $200 each month and the card charges 20 percent APR (compounded monthly), how long will it take him to pay off the debt?

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 2.5 percent APR interest rate. After the second year, the mortgage interest charged increases to 4.25 percent APR. What is the effective interest rate in the first two years? What is the effective interest rate after the second year?

To compute the present or future value of an annuity due, one computes the value of an ordinary annuity and then

Say that you purchase a house for $150,000 by getting a mortgage for $135,000 and paying a $15,000 down payment. If you get a 15-year mortgage with a 6 percent interest rate, what would the loan balance be in seven years?

Say that you purchase a house for $150,000 by getting a mortgage for $135,000 and paying a $15,000 down payment. If you get a 15-year mortgage with a 6 percent interest rate, what are the monthly payments?

Chase purchased a $30,000 car three years ago using a 10 percent, 5-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.)

Consider that you are 30 years old and have just changed to a new job. You have $91,000 in the retirement plan from your former employer. You can roll that money into the retirement plan of the new employer. You will also contribute $4,800 each year into your new employer's plan. If the rolled-over money and the new contributions both earn a 7 percent return, how much should you expect to have when you retire in 38 years?

What annual interest rate would you need to earn if you wanted a $500 per month contribution to grow to $27,050 in four years?

What is the future value of an $800 annuity payment over 15 years if the interest rates are 6 percent?

Isaac realizes that he charged too much on his credit card and has racked up $5,000 in debt. If he can pay $225 each month and the card charges 17.55 percent APR (compounded monthly), how long will it take him to pay off the credit card?

Jane has been saving $500 in her retirement account each month for the last 20 years and plans to continue contributing $500 each month for the next 20 years. Her account has been earning an 8 percent annual interest rate and she expects to earn the same rate for the next 20 years. Her twin brother, Hal, has not saved anything for the last 20 years. Due to sibling rivalry, he wants to have as much as Jane is expected to have at the end of 20 years. If Hal expects to earn the same annual interest rate as Jane, how much must Hal save each month to achieve his goal?

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?

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 daily (365 day year). The second credit card charges 18 percent APR and compounds semiannually. What is the effective annual rate of the cheaper card?

You started your first job after graduating from college. Your company offers a retirement plan for which the company contributes 50 percent of what you contribute each year. You expect to contribute $2,000 per year from your salary. You decide to invest the contributions in assets that you expect to earn 10 percent per year. If you plan to retire in 40 years, how big will you expect that retirement account to be?

A small business owner visits his bank to ask for a loan. The owner states that she can repay a loan at $1,250 per month for the next three years and then $500 per month for two years after that. If the bank is charging customers 12 percent APR, how much would it be willing to lend the business owner?

Compute the present value of a $2,500 deposit in year 4 and another $10,000 deposit at the end of year 8 if interest rates are 15 percent.

A car company is offering a choice of deals. You can receive $600 cash back on the purchase, or a 2 percent APR, 4-year loan. The price of the car is $18,900 and you could obtain a 4-year loan from your credit union at 6 percent APR. What is the monthly payment of each deal?