Exam 5: Time Value of Money

Last Christmas, Danny received an annual bonus of $1,500. These annual bonuses are expected to grow by 5 percent for the next 5 years. How much will Danny have at the end of the fifth year if he invests his Christmas bonuses (including the most recent bonus) in a project paying 8 percent per year?

What is the highest effective rate attainable with a 12 percent nominal rate?

Find the present value of the following stream of cash flows, assuming that the firm's opportunity cost is 14 percent.

Nico is 30 years old and will retire at age 65. He will receive retirement benefits but the benefits are not going to be enough to make a comfortable retirement life for him. Nico has estimated that an additional $25,000 a year over his retirement benefits will allow him to have a satisfactory life. How much should Nico deposit today in an account paying 6 percent interest to meet his goal? Assume Nico will have 15 years of retirement.

When computing an interest or growth rate, the rate will increase the larger the future value, holding present value and the number of periods constant.

Colin has inherited $6,000 from the death of Grandma Anna. He would like to use this money to buy his mom Hayley a new scooter costing $7,000 2 years from now. Will Colin have enough money to buy the gift if he deposits his money in an account paying 8 percent compounded semi-annually?

A lottery administrator has just completed the state's most recent $50 million lottery. Receipts from lottery sales were $50 million and the payout will be $5 million at the end of each year for 10 years. The expenses of running the lottery were $800,000. The state can earn an annual compound rate of 8 percent on any funds invested. (a) Calculate the gross profit to the state from this lottery. (b) Calculate the net profit to the state from this lottery (no taxes).

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

Calculate the future value of $10,000 received today and deposited for six years in an account which pays interest of 12 percent compounded quarterly.

Bill plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If Bill can earn 12 percent on his contributions, how much will he have at the end of the twentieth year?

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.

Xiao Xin is planning to accumulate $40,000 by the end of 5 years by making 5 equal annual deposits. If she plans to make her first deposit today and can earn an annual compound rate of 9 percent on her investment, how much must each deposit be in order to accumulate the $40,000?

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 8 percent on its investments.

The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of the next 10 years is

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

You have provided your friend with a service worth $8,500. Your friend offers you the following cash flow instead of paying $8,500 today. Should you accept his offer if your opportunity cost is 8 percent?

The present value of $100 received at the end of year 1, $200 received at the end of year 2, and $300 received at the end of year 3, assuming an opportunity cost of 13 percent, is

The future value of a dollar ________ as the interest rate increases and ________ the farther in the future an initial deposit is to be received.

The present value of a $25,000 perpetuity at a 14 percent discount rate is

An annuity due is an amount that occurs at the beginning of each period.