Exam 5: The Time Value of Money

Congratulations! You are the proud winner of the multi-state Sour Ball Lottery.You are to receive $2,000,000 at the end of each year for the next 20 years.While the Lottery Commission refers to this as a $40,000,000 jackpot,if you choose the "cash option" they will give you much less than that; you can receive a lump sum payment today equal to the present value of the ordinary annuity instead of the 20 annual payments.If the discount rate that the Lottery Commission uses to determine the lump sum payoff is 7%,what is your payoff if you select the cash option?

If you put $2,000 in a savings account that yields 8% compounded semiannually,how much money will you have in the account in 20 years (rounded to nearest $10)?

A bond will pay $5,000 at maturity in 9 years.It also makes semiannual interest payments of $400 until maturity.If the discount rate is 7% compounded semiannually,what should be the market price of the bond?

$10,000 invested at 10% per year for 5 years earns interest equal to $6,105.10; therefore,$10,000 invested at 10% per year for 10 years will earn interest equal to $12,210.20 (2 times $6,105.10).

If the future value of an annuity is known,then the present value of the annuity can be found using the present value of a lump sum formula,even if the amount of each annuity payment is unknown.

Today is your 21st birthday and your bank account balance is $25,000.Your account is earning 6.5% interest compounded quarterly.How much will be in the account on your 50th birthday?

To evaluate or compare investment proposals,we must adjust the value of all cash flows to a common date.

You borrow $30,000 and agree to pay it off with one lump sum payment of $40,000 in 6 years.What annual rate of interest will you be charged?

The value of a bond investment,which provides fixed interest payments,will increase when discounted at an 8% rate rather than at an 11% rate.

U.S.Savings Bonds are sold at a discount.The face value of the bond represents its value on its future maturity date.Therefore,

Andre's wonderful parents established a college savings plan for him when he was born.They deposited $50 into the account on the last day of each month.The account has earned 10.9% compounded monthly,tax-free.How much can they withdraw on his 18th birthday to spend on his education?

What is the value on 1/1/13 of the following cash flows: Use a 7% discount rate,and round your answer to the nearest $10.

If you want to have $5,000 in 10 years,how much money must you put in a savings account today? (Assume that the savings account pays 4% and it is compounded daily; round to the nearest $1).

Inputs using an Excel spreadsheet are almost identical to those on a financial calculator,except the interest rate is entered either as a decimal (.05)or a whole number followed by a % sign (5%)rather than simply a whole number (5)as you would enter using a financial calculator.

You are currently 25 years of age.You have developed a lifetime budget that includes $50,000 at age 40 for a college fund for your kids and $25,000 per year for 20 years to supplement your retirement,the first payment on your 60th birthday and the last payment on your 79th birthday.You open an investment account on your 25th birthday that promises to pay 9% interest compounded annually.You want to deposit equal annual amounts into the account every year on your birthday,starting today (your 25th birthday)and continuing until you are 40 years old (i.e.,the last deposit is made on your 40th birthday).How much will each deposit have to be if you want to meet your financial goals?

Today is your 30th birthday and you must choose between two retirement options.The first option will provide you with 10 equal annual payments of $100,000 beginning on your 65th birthday.The second option will provide you with one payment of $1,000,000 on your 70th birthday.If the interest rate is 6 percent per year and you are assured of living to at least 80 years of age,which option is better?

When solving time value of money problems on a financial calculator,you must select the "end mode" when you enter the final year's cash flow.

You want $20,000 in 5 years to take your spouse on a second honeymoon.Your investment account earns 7% compounded semiannually.How much money must you put in the investment account today? (Round to the nearest $1.)

How much would you be willing to pay (rounded to the nearest dollar)for a 20-year ordinary annuity if the payments are $4,500 per year and you want to earn a rate of return equal to 5.5% per year?

At an annual interest rate of 9%,an initial sum of money will double approximately every 8 years.