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

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?

Your current $95,000 mortgage calls for monthly payments over 30 years at an annual interest rate of 6 percent. If you pay an additional $50 each month beginning with the first payment, how soon do you pay off your mortgage?

Given a 6 percent interest rate, compute the present value of deposits made in years 1, 2, 3, and 4 of $1,200, $1,400, $1,400, and $1,500.

Bank A charges a 7.50 percent annual percentage rate and interest is due at the end of the year. Bank B charges a 6.95 percent annual percentage rate and interest must be paid monthly. What is the effective annual rate charged by each bank?

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?

What is the amount of interest and repayment of principal balance in month 2 for a loan of $10,000, paid monthly over five years at a 7 percent APR?

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?

Compounding monthly versus annually causes the interest rate to be effectively higher, and thus the future value

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?

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?

Jasmine has decided that she wants to build enough retirement wealth that, if invested at 6 percent per year, will provide her with $3,000 of monthly income for 30 years. To date, she has saved nothing but she still has 25 years until she retires. Jasmine believes that she can earn 6 percent on her investments until she retires. How much money does she need to contribute per month to reach her goal?

You win $1,000 today, which happens to be your 20th 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?

If you start making $25 monthly contributions today and continue them for four years, what is their future value if the compounding rate is 6 percent APR? What is the present value of this annuity?

Level sets of frequent, consistent cash flows are called

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?

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?

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?

You wish to buy a $30,000 car. The dealer offers you a 5-year loan with a 9 percent APR. What are the monthly payments? What is the monthly payment if you paid interest only?

In order to discount multiple cash flows to the present, one would use

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.