Exam 5: Time Value of Money

The New York Soccer Association would like to accumulate $10,000 by the end of 4 years from now to finance a big soccer weekend for its members. The Association currently has $2,500 and wishes to raise the balance by arranging annual fund-raising events. How much money should they raise at each annual fund-raising event assuming 8 percent rate of interest?

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

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.

Danny Joe borrows $10,500 from the bank at 11 percent annually compounded interest to be repaid in six equal annual installments. The interest paid in the first year is

Find the present value of the following stream of cash flows, assuming that the firm's opportunity cost is 25 percent.

In general, with an amortized loan, the payment amount remains constant over the life of the loan, the principal portion of each payment grows over the life of the loan, and the interest portion of each payment grows over the life of the loan.

The present value of an ordinary annuity of $2,350 each year for eight years, assuming an opportunity cost of 11 percent, is

Everything else being equal, the higher the interest rate, the higher the future value.

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

Detta borrows $20,000 from the bank. For a five-year loan, the bank requires annual end-of-year payments of $4,878.05. The annual interest rate on the loan is

Rita borrows $4,500 from the bank at 9 percent annually compounded interest to be repaid in three equal annual installments. The interest paid in the third year 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?

Entertainer's Aid plans five annual colossal concerts, each in a different nation's capital. The concerts will raise funds for an endowment which would provide the World Wide Hunger Fund with $3,000,000 per year into perpetuity. The endowment will be given at the end of the fifth year. The rate of interest is expected to be 9 percent in all future periods. How much must Entertainer's Aid deposit each year to accumulate to the required amount?

If you expect to retire in 30 years, are currently comfortable living on $50,000 per year and expect inflation to average 3% over the next 30 years, what amount of annual income will you need to live at the same comfort level in 30 years?

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 college year 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.

Brian borrows $5,000 from a bank at 8 percent annually compounded interest to be repaid in five annual installments. Calculate the principal paid in the third year.

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?

The nominal and effective rates are equivalent for annual compounding.

A wealthy industrialist wishes to establish a $2,000,000 trust fund which will provide income for his grandchild into perpetuity. He stipulates in the trust agreement that the principal may not be distributed. The grandchild may only receive the interest earned. If the interest rate earned on the trust is expected to be at least 7 percent in all future periods, how much income will the grandchild receive each year?

A deep-discount bond can be purchased for $312 and in 20 years it will be worth $1,000. What is the rate of interest on the bond?