Exam 5: Time Value of Money

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

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 ________.

Find the present value of the following stream of cash flows assuming an opportunity cost of 9 percent.

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 certain investment that costs $10,000 today promises to pay you $10,500 in five years.This investment ________.

Ashley is planning to attend college when she graduates from high school 7 years from now.She anticipates that she will need $20,000 at the beginning of each of the four college years to pay for tuition and fees,and have some spending money (i.e.,she needs to be able to withdraw $20,000 from savings four times,with the first withdrawal taking place 7 years from now).Ashley's father has promised to help her save for college by making 7 deposits of $7,000 each into an investment accounting earning 8 percent interest.His first payment comes a year from today.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.

Find the present value of the following stream of cash flows assuming an opportunity cost of 25 percent.

Your current income is $50,000 per year,and you would like to maintain your current standard of living (i.e.,your purchasing power)when you retire.If you expect to retire in 30 years 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?

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?

The future value of an ordinary annuity of $1,000 each year for 10 years,deposited at 3 percent,is ________.

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

The rate of return earned on an investment of $50,000 today that guarantees an annuity of $10,489 for six years is approximately ________.

A perpetuity will pay you $100 starting next year and continuing at that level forever.The appropriate discount rate for the perpetuity is 10%.Calculate the present value of (1)the infinite stream of payments,i.e.,the entire perpetuity,and (2)the first 20 payments.Compare these two present values and comment on what they can tell you about the present value of the perpetuity's payments in the very distant future (i.e.,payments made later than 20 years in the future).

Calculate the future value of an annuity of $5,000 each year for eight years,deposited at 6 percent.

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 ________.

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 effective rate of interest and compounding frequency are inversely related.

The future value of $100 received today and deposited in an account for four years paying semiannual interest of 6 percent is ________.

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

China Manufacturing Agents,Inc.is preparing a five-year plan.Today,sales are $1,000,000.If the growth rate in sales is projected to be 10 percent over the next five years,what will the dollar amount of sales be in year five?