Exam 5: Time Value of Money

Everything else being equal, the higher the discount rate, the higher the present value.

How long would it take for Nico to save an adequate amount for retirement if he deposits $40,000 per year into an account beginning one year from today that pays 12 percent per year if he wishes to have a total of $1,000,000 at retirement?

The rate of interest actually paid or earned, also called the annual percentage rate (APR), is the ________ interest rate.

Ken borrows $15,000 from a bank at 10 percent annually compounded interest to be repaid in six equal installments. Calculate the interest paid in the second year.

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?

The effective rate of interest and compounding frequency are inversely related.

You are considering the purchase of new equipment for your company and you have narrowed down the possibilities to two models which perform equally well. However, the method of paying for the two models is different. Model A requires $5,000 per year payment for the next five years. Model B requires the following payment schedule. Which model should you buy if your opportunity cost is 8 percent?

Dorothy borrows $10,000 from the bank. For a four-year loan, the bank requires annual end-of-year payments of $3,223.73. The annual interest rate on the loan is ________.

A firm wishes to establish a fund which, in 10 years, will accumulate to $10,000,000. The fund will be used to repay an outstanding bond issue. The firm plans to make deposits, which will earn 12 percent, to this fund at the end of each of the 10 years prior to maturity of the bond. How large must these deposits be to accumulate to $10,000,000?

Ms. Day needs $20,000 to buy her dream car. In her search for the best (low cost) loan, she has gathered the following information from three local banks. Which bank would you recommend Ms. Day borrow from?

To expand its operation, the International Tools Inc. (ITI) has applied for a $3,500,000 loan from the International Bank. According to ITI's financial manager, the company can only afford a maximum yearly loan payment of $1,000,000. The bank has offered ITI, 1) a 3-year loan with a 10 percent interest rate, 2) a 4-year loan with a 11 percent interest rate, or 3) a 5-year loan with a 12 percent interest rate. (a) Compute the loan payment under each option. (b) Which option should the company choose?

Nico makes annual end-of-year payments of $5,043.71 on a four-year loan with an interest rate of 13 percent. The original principal amount was ________.

Alexis owns stock in a company which has consistently paid a growing dividend over the last 10 years. The first year Alexis owned the stock, she received $4.50 per share and in the 10th year, she received $4.92 per share. What is the growth rate of the dividends over the last 10 years?

Find the future value at the end of year 3 of the following stream of cash flows received at the end of each year, assuming the firm can earn 17 percent on its investments.

Nico establishes a seven-year, 8 percent loan with a bank requiring annual end-of-year payments of $960.43. Calculate the original principal amount.

What is the rate of return on an investment of $16,278 if the company expects to receive $3,000 per year for the next 10 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.

The effective rate of interest differs from the nominal rate of interest in that it reflects the impact of compounding frequency.

Dan plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 10 years. If Dan can earn 10 percent on his contributions, how much will he have at the end of the tenth year?

The future value of $200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is ________.