Exam 4: The Time Value of Money

The Desai Company just borrowed $1,000,000 for 3 years at a quoted rate of 8 percent,quarterly compounding.The loan is to be amortized in end-of-quarter payments over its 3-year life.How much interest (in dollars)will your company have to pay during the second quarter?

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

Bank A offers a 2-year certificate of deposit (CD)that pays 10 percent compounded annually.Bank B offers a 2-year CD that is compounded semi-annually.The CDs have identical risk.What is the stated,or simple,rate that Bank B would have to offer to make you indifferent between the two investments?

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 currently 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?

What is the future value of a 5-year ordinary annuity with annual payments of $200,evaluated at a 15 percent interest rate?

Your employer has agreed to make 80 quarterly payments of $400 each into a trust account to fund your early retirement.The first payment will be made 3 months from now.At the end of 20 years (80 payments),you will be paid 10 equal annual payments,with the first payment to be made at the beginning of Year 21 (or the end of Year 20).The funds will be invested at a simple rate of 8.0 percent,quarterly compounding,during both the accumulation and the distribution periods.How large will each of your 10 receipts be? (Hint: You must find the EAR and use it in one of your calculations.)

The greater the number of compounding periods within a year,the greater the future value of a lump sum invested initially,and the greater the present value of a given lump sum to be received at maturity.

All else equal,the future value of a lump-sum amount invested today will increase if the

Your father,who is 60,plans to retire in 2 years,and he expects to live independently for 3 years.Suppose your father wants to have a real income of $40,000 in today's dollars in each year after he retires.His retirement income will start the day he retires,2 years from today,and he will receive a total of 3 retirement payments.Inflation is expected to be constant at 5 percent.Your father has $100,000 in savings now,and he can earn 8 percent on savings now and in the future.How much must he save each year,starting today,to meet his retirement goals?

Everything else equal,which of the following conditions will result in the lowest present value of an amount to be received in the future?

If you buy a factory for $250,000 and the terms are 20 percent down,the balance to be paid off over 30 years at a 12 percent rate of interest on the unpaid balance,what are the 30 equal annual payments?

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

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

An amortized loan is a loan that requires equal payments over its life; its payments include both interest and repayment of the debt.

You want to buy a Nissan 350Z on your 27th birthday.You have priced these cars and found that they currently sell for $30,000.You believe that the price will increase by 5 percent per year until you are ready to buy.You can presently invest to earn 14 percent.If you just turned 20 years old,how much must you invest at the end of each of the next 7 years to be able to purchase the Nissan in 7 years?

Solving for the interest rate associated with a stream of uneven cash flows,without the use of a calculator,usually involves a trial and error process.

Your lease calls for payments of $500 at the end of each month for the next 12 months.Now your landlord offers you a new 1-year lease which calls for zero rent for 3 months,then rental payments of $700 at the end of each month for the next 9 months.You keep your money in a bank time deposit that pays a simple annual rate of 5 percent.By what amount would your net worth change if you accept the new lease? (Hint: Your return per month is 5%/12 = 0.4166667%.)

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?

You will receive a $100 annual perpetuity,the first payment to be received now,at Year 0,a $300 annual perpetuity payable starting at the end of Year 5,and a $200 semiannual (2 payments per year)perpetuity payable starting midway through Year 10.If you require an effective annual interest rate of 14.49 percent,what is the present value of all three perpetuities together at Year 0? (Hint: The semiannual annuity can be thought of as two annual annuities.)

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 which 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?