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

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?

A perpetuity, a special form of annuity, pays cash flows

When interest rates are lower, borrowers can

Jane has been saving $200 in her retirement account each month for the last 20 years and plans to continue contributing $200 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?

Compute the future value in year 10 of a $1,000 deposit in year 1, and another $1,500 deposit at the end of year 4 using an 8 percent interest rate.

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?

Jane has been saving $450 in her retirement account each month for the last 20 years and plans to continue contributing $450 each month for the next 20 years. Her account has been earning a 9 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?

Payday loans are very short-term loans that charge very high interest rates. You can borrow $550 today and repay $675 in two weeks. What is the compounded annual rate implied by this 22.73 percent rate charged for only two weeks?

Your company borrows $275,000 today to fund its growth initiatives. It must repay the bank in five annual payments of $76,300 at the end of each year. What annual interest rate is your firm paying?

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.

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?

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.)

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

When moving from the left to the right of a time line, we are using

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 have reviewed your budget and determine that the most you can afford on a car loan is $550 per month. What is the most you can borrow if interest rates are 6 percent and you can pay the loan over three years?

What annual interest rate would you need to earn if you wanted a $1,250 per month contribution to grow to $65,000 in three years?

What is the present value, when interest rates are 10 percent, of a $75 payment made every year forever?

You have reviewed your budget and determine that the most you can afford on a car loan is $455 per month. What is the most you can borrow if interest rates are 7 percent and you can pay the loan over four years?

A car company is offering a choice of deals. You can receive $4,000 cash back on the purchase, or a 0 percent APR, 4-year loan. The price of the car is $40,000 and you could obtain a 4-year loan from your credit union, at 6 percent APR. Which deal is cheaper?