Exam 4: Time Value of Money

You can deposit your savings at the Darlington National Bank, which offers to pay 12.6 percent interest compounded monthly, or at the Bartlett Bank, which will pay interest of 11.5 percent compounded daily.(Assume 365 days in a year.) Which bank offers the higher effective annual rate?

You have the opportunity to buy a perpetuity which pays $1,000 annually.Your required rate of return on this investment is 15 percent.You should be essentially indifferent to buying or not buying the investment if it were offered at a price of

Vegit Corporation needs to borrow funds to support operations during the summer.Vegit's CFO is trying to decide whether to borrow from the Bank of Florida or the Bank of Georgia.The loan offered by Bank of Florida has a 12.5 percent simple interest rate with annual interest payments, whereas the loan offered by the Bank of Georgia has a 12 percent simple interest rate with monthly payments.Which bank should Vegit use for the loan?

As the discount rate increases without limit, the present value of the future cash inflows

Suppose someone offered you your choice of two equally risky annuities, each paying $5,000 per year for 5 years. One is an annuity due, while the other is a regular (or deferred) annuity.If you are a rational wealth-maximizing investor which annuity would you choose?

Assume that you are graduating, that you plan to work for 4 years, and then to go to law school for 3 years.Right now, going to law school would require $17,000 per year (for tuition, books, living expenses, etc.), but you expect this cost to rise by 8 percent per year in all future years.You now have $25,000 invested in an investment account which pays a simple annual rate of 9 percent, quarterly compounding, and you expect that rate of return to continue into the future.You want to maintain the same standard of living while in law school that $17,000 per year would currently provide.You plan to save and to make 4 equal payments (deposits) which will be added to your account at the end of each of the next 4 years; these new deposits will earn the same rate as your investment account currently earns. How large must each of the 4 payments be in order to permit you to make 3 withdrawals, at the beginning of each of your 3 years in law school? (Note: (1) The first payment is made a year from today and the last payment 4 years from today, (2) the first withdrawal is made 4 years from today, and (3) the withdrawals will not be of a constant amount.)

Assume you are to receive a 20-year annuity with annual payments of $50.The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 20.You will invest each payment in an account that pays 10 percent.What will be the value in your account at the end of Year 30?

Assume that you inherited some money.A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling some securities which call for four payments, $50 at the end of each of the next 3 years, plus a payment of $1,050 at the end of Year 4.Your friend says she can get you some of these securities at a cost of $900 each.Your money is now invested in a bank that pays an 8 percent simple (quoted) interest rate, but with quarterly compounding.You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit.You must calculate the value of the securities to decide whether they are a good investment.What is their present value to you?

You want to borrow $1,000 from a friend for one year, and you propose to pay her $1,120 at the end of the year. She agrees to lend you the $1,000, but she wants you to pay her $10 of interest at the end of each of the first 11 months plus $1,010 at the end of the 12th month.How much higher is the effective annual rate under your friend's proposal than under your proposal?

You have just borrowed $20,000 to buy a new car.The loan agreement calls for 60 monthly payments of $444.89 ea to begin one month from today.If the interest is compounded monthly, then what is the effective annual rate on this loan?

Cash flow time lines are used primarily for decisions involving paying off debt or investing in financial securities. They cannot be used when making decisions about investments in physical assets.

Sarah is thinking about purchasing an investment from HiBond Investing.If she buys the investment, Sarah will receive $100 every three months for five years.The first $100 payment will be made as soon as she purchases the investment.If Sarah's required rate of return is 16 percent, to the nearest dollar, how much should she be willing to pay for this investment?

You are currently saving for your child's college education.The current cost of college is $10,000 a year.You expect that college costs will continue to increase at a rate of 5 percent a year.Your child is scheduled to begin attending a four-year college 10 years from now .You currentl have $25,000 in an account which earns 6 percent after taxes.You would like to have all of the necessary savings by the time your child enters college, and you would like to contribute a constant amount at the beginning of each of the next 10 years in order to provide the necessary amount.(You want to make 10 equal contributions starting in Year 0 and ending at Year 9.) How much should you contribute to the account each year in order to fully provide for your child's education?

Because we usually assume positive interest rates in time value analyses, the present value of a three-year annuity will always be less than the future value of a single lump sum, if the sum of the annuity payments equals the original lump sum investment.

The difference between the PV of an annuity due and the PV of an ordinary annuity is that each of the payments of the annuity due is discounted by one more year.

Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will

You are considering an investment in a 40-year security.The security will pay $25 a year at the end of each of the first three years.The security will then pay $30 a year at the end of each of the next 20 years.The simple interest rate is assumed to be 8 percent, and the current price (present value) of the security is $360.39.Given this information, what is the equal annual payment to be received from Year 24 through Year 40 (i.e., for 17 years)?

What is the effective annual return (EAR) for an investment that pays 10 percent compounded annually?

One of the potential benefits of investing early for retirement is that an investor can receive greater benefits from the compounding of interest.

Your company must make payments of $100,000 each year for 10 years, with the first payment to be made 10 years from today.To prepare for these payments, your company must make 10 equal annual deposits into an account whic pays a simple interest rate of 7 percent, daily compounding (360-day year).Funds will remain in the account during both the accumulation period (the first 10 years) and the distribution period (the last 10 years), and the same interest rate will be earned throughout the entire 20 years.The first deposit will be made immediately.How large must each deposit be?