Exam 28: Time Value of Money

Suppose Randy Jones plans to invest $1,000.He can earn an effective annual rate of 5% on Security A,while Security B has an effective annual rate of 12%.After 11 years,the compounded value of Security B should be somewhat less than twice the compounded value of Security A.(Ignore risk,and assume that compounding occurs annually.)

How much would $1,growing at 3.5% per year,be worth after 75 years?

If we are given a periodic interest rate,say a monthly rate,we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.

A "growing annuity" is a cash flow stream that grows at a constant rate for a specified number of periods.

Scott and Linda have been saving to pay for their daughter Casie's college education.Casie just turned 10 at (t = 0),and she will be entering college 8 years from now (at t = 8).College tuition and expenses at State U.are currently $14,500 a year,but they are expected to increase at a rate of 3.5% a year.Ellen should graduate in 4 years⎯if she takes longer or wants to go to graduate school,she will be on her own.Tuition and other costs will be due at the beginning of each school year (at t = 8,9,10,and 11). So far,Scott and Linda have accumulated $15,000 in their college savings account (at t = 0).Their long-run financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1,2,3,and 4).Then they plan to make 3 equal annual contributions in each of the following years,t = 5,6,and 7.They expect their investment account to earn 9%.How large must the annual payments at t = 5,6,and 7 be to cover Casie's anticipated college costs?

Geraldine was injured in a car accident,and the insurance company has offered her the choice of $25,000 per year for 15 years,with the first payment being made today,or a lump sum.If a fair return is 7.5%,how large must the lump sum be to leave her as well off financially as with the annuity?

You want to purchase a motorcycle 4 years from now,and you plan to save $3,500 per year,beginning immediately.You will make 4 deposits in an account that pays 5.7% interest.Under these assumptions,how much will you have 4 years from today?

Which of the following statements regarding a 20-year (240-month)$225,000,fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

Your 75-year-old grandmother expects to live for another 15 years.She currently has $1,000,000 of savings,which is invested to earn a guaranteed 5% rate of return.If inflation averages 2% per year,how much can she withdraw (to the nearest dollar)at the beginning of each year and keep the withdrawals constant in real terms,i.e.,growing at the same rate as inflation and thus enabling her to maintain a constant standard of living?

Now that your uncle has decided to retire,he wants to buy an annuity that will provide him with $85,000 of income a year for 25 years,with the first payment coming immediately.The going rate on such annuities is 5.15%.How much would it cost him to buy the annuity today?

Disregarding risk,if money has time value,it is impossible for the future value of a given sum to exceed its present value.

Southwestern Bank offers to lend you $50,000 at a nominal rate of 6.5%,compounded monthly.The loan (principal plus interest)must be repaid at the end of the year.Woodburn Bank also offers to lend you the $50,000,but it will charge an annual rate of 7.0%,with no interest due until the end of the year.How much higher or lower is the effective annual rate charged by Woodburn versus the rate charged by Southwestern?

The greater the number of compounding periods within a year,then (1)the greater the future value of a lump sum investment at Time 0 and (2)the greater the present value of a given lump sum to be received at some future date.

As a result of compounding,the effective annual rate on a bank deposit (or a loan)is always equal to or less than the nominal rate on the deposit (or loan).

Your bank offers a savings account that pays 3.5% interest,compounded annually.If you invest $1,000 in the account,then how much will it be worth at the end of 25 years?

Your older brother turned 35 today,and he is planning to save $7,000 per year for retirement,with the first deposit to be made one year from today.He will invest in a mutual fund that's expected to provide a return of 7.5% per year.He plans to retire 30 years from today,when he turns 65,and he expects to live for 25 years after retirement,to age 90.Under these assumptions,how much can he spend each year after he retires? His first withdrawal will be made at the end of his first retirement year.

A time line is not meaningful unless all cash flows occur annually.

Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

You are considering investing in a European bank account that pays a nominal annual rate of 18%,compounded monthly.If you invest $5,000 at the beginning of each month,how many months would it take for your account to grow to $250,000? Round fractional months up.

Cochrane Associate's net sales last year were $525 million.If sales grow at 7.5% per year,how large (in millions)will they be 8 years later?