Exam 5: Time Value of Money

Tom is evaluating the growth rate in dividends of a company over the past 6 years. What is the annual compound growth rate if the dividends are as follows:

If the present value of a perpetual income stream is increasing, the discount rate must be ________.

What annual rate of return would Grandma Zoe need to earn if she deposits $1,000 per month into an account beginning one month from today in order to have a total of $1,000,000 in 30 years?

Calculate the present value of a $10,000 perpetuity at a 6 percent discount rate.

The effective rate of interest is the contractual rate of interest charged by a lender or promised by a borrower.

A(n) ________ is an annuity with an infinite life making continual annual payments.

Ashley is planning to attend college when she graduates from high school 7 years from now. She anticipates that she will need $10,000 at the beginning of each of the four college years to pay for tuition and fees, and have some spending money. Ashley has made an arrangement with her father to do the household chores if her dad deposits $3,500 at the end of each year for the next 7 years in a bank account paying 8 percent interest. Will there be enough money in the account for Ashley to pay for her college expenses? Assume the rate of interest stays at 8 percent during the college years.

When computing the number of deposits needed to accumulate to a future sum, it will take longer if the interest rate decreases, holding the future value and deposit size constant.

Ashley owns stock in a company which has consistently paid a growing dividend over the last five years. The first year Ashley owned the stock, she received $1.71 per share and in the fifth year, she received $2.89 per share. What is the growth rate of the dividends over the last five years?

Zheng Sen wishes to accumulate $1 million by the end of 20 years by making equal annual end-of-year deposits over the next 20 years. If Zheng Sen can earn 10 percent on his investments, how much must he deposit at the end of each year?

Otto is planning for his son's college education to begin ten years from today. He estimates the end-of-the-year tuition, books, and living expenses to be $10,000 per year for a four-year degree. How much must Otto deposit today, at an interest rate of 12 percent, for his son to be able to withdraw $10,000 per year for four years of college?

Jeanne has just graduated from high school and has received an award for $5,000. She would like to deposit the money in an interest earning account until she graduates from college bank B pays 8 percent interest compounded semiannually. Which is the better offer, and how much will Jeanne have upon graduation from college?

The nominal (stated) annual rate is the rate of interest actually paid or earned.

The future value of $200 received today and deposited at 8 percent compounded semiannually for three years is ________.

What annual rate of return would Jia need to earn if she deposits $20,000 per year into an account beginning one year from today in order to have a total of $1,000,000 in 30 years?

The following table presents the Sally's Silly Service Company's net earnings for the past six years. Compute the growth rate in the company's earnings.

$1,200 is received at the beginning of year 1, $2,200 is received at the beginning of year 2, and $3,300 is received at the beginning of year 3. If these cash flows are deposited at 12 percent, their combined future value at the end of year 3 is ________.

Ten years ago, Tom purchased a painting for $300. The painting is now worth $1,020. Tom could have deposited $300 in a savings account paying 12 percent interest compounded annually. Which of these two options would have provided Tom with a higher return?

Dan and Jia are newlyweds and have just purchased a condominium for $70,000. Since the condo is very small, they hope to move into a single-family house in 5 years. How much will their condo worth in 5 years if inflation is expected to be 8 percent?

A college received a contribution to its endowment fund of $2 million. It can never touch the principal, but can use the earnings. At an assumed interest rate of 9.5 percent, how much can the college earn to help its operations each year?