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

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?

Which of the following will increase the future value of an annuity?

Compute the future value in year 12 of a $2,000 deposit in year 3 and another $4,000 deposit at the end of year 5 using a 10 percent interest rate.

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?

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 is the present value of a $600 annuity payment over 4 years if interest rates are 6 percent?

A loan is offered with monthly payments and a 14.5 percent APR. What is the loan's effective annual rate (EAR)?

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?

You wish to buy a $15,000 car. The dealer offers you a 4-year loan with a 9 percent APR. What are the monthly payments?

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?

When you get your credit card bill, it will offer a minimum payment, which:

Phoebe realizes that she has charged too much on her credit card and has racked up $7,000 in debt. If she can pay $200 each month and the card charges 17 percent APR (compounded monthly), how long will it take her to pay off the debt?

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?

Given a 7 percent interest rate, compute the year 6 future value if deposits of $2,500 and $1,500 are made in years 2 and 3, respectively, and a withdrawal of $900 is made in year 4.

Given a 10 percent interest rate, compute the year 9 future value if deposits of $10,000 and $20,000 are made in years 1 and 5 respectively, and a withdrawal of $5,000 is made in year 7.

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.)

Joey realizes that he has charged too much on his credit card and has racked up $3,000 in debt. If he can pay $150 each month and the card charges 18 percent APR (compounded monthly), how long will it take him to pay off the debt?

You win $1,000 today, which happens to be your 20^th birthday. You decide to deposit this money in an account and plan to add $1,000 to it each year on your birthday beginning one year from today. If you earn 10 percent per year in the account, how long will it take to grow to $750,000?

You started your first job after graduating from college. Your company offers a retirement plan for which the company contributes 25 percent of what you contribute each year. You expect to contribute $5,000 per year from your salary. You decide to invest the contributions in assets that you expect to earn 8 percent per year. If you plan to retire in 35 years, how big will you expect that retirement account to be?

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: