Exam 5: Time Value of Money

For any interest rate and for any period of time,the more frequently interest is compounded,the greater the amount of money that has to be invested today in order to accumulate a given future amount.

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?

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 ________.

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?

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

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

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

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

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?

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.

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?

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?

Gina has planned to start her college education four years from now.To pay for her college education,she has decided to save $1,000 a quarter for the next four years in a bank account paying 12 percent interest.How much will she have at the end of the fourth year?

The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity for interest rates greater than zero.

Aunt Butch borrows $19,500 from the bank at 8 percent annually compounded interest to be repaid in 10 equal annual installments.The interest paid in the third year is ________.

The amount of money that would have to be invested today at a given interest rate over a specified period in order to equal a future amount is called ________.

What is the rate of return on an investment of $124,090 if the company expects to receive $10,000 per year for the next 30 years?

The future value of an annuity of $1,000 each quarter for 10 years,deposited at 12 percent compounded quarterly is ________.

Aunt Tillie has deposited $33,000 today in an account which will earn 10 percent annually.She plans to leave the funds in this account for seven years earning interest.If the goal of this deposit is to cover a future obligation of $65,000,what recommendation would you make to Aunt Tillie?

Jia borrows $50,000 at 10 percent annually compounded interest to be repaid in four equal annual installments.The actual end-of-year loan payment is ________.