Exam 3

A deferred annuity will pay you $500 at the end of each year for 10 years, however the first payment will not be made until three years from today (payments will be made at the end of years 3 through 12). What amount will you have to deposit today to fund this deferred annuity? Use an 8% discount rate and round your answer to the nearest $100.

$2,900

You are thinking of buying a craft emporium. It is expected to generate cash flows of $30,000 per year in years 1 through 5, and $40,000 per year in years 6 through 10. If the appropriate discount rate is 8%, what amount are you willing to pay for the emporium?

$228,476

If you put $100 in a savings account at the beginning of each month for 10 years, how much money will be in the account at the end of the 10th year? Assume that the account earns 12% compounded monthly.

$23,234 (Hint: Adjust for N and I/Y)

What is the present value of an annuity of $4,000 received at the beginning of each year for the next eight years? The first payment will be received today, and the discount rate is 9% (round to nearest $1)

$24,132

You charged $1,000 on your credit card for Christmas presents. Your credit card company charges you 26% annual interest, compounded monthly. If you make the minimum payments of $25 per month, how long will it take (to the nearest month) to pay off your balance?

94 months (Hint: Adjust for N and I/Y)

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?

$53,777 (Hint: Compare with 31!)

A zero coupon bond pays no annual coupon interest payments. When it matures at the end of 7.5 years it pays out $1,000. If investors wish to earn 2.35% per year on this bond investment, what is the current price of the bond? (Round to the nearest dollar.)

$840

What is the present value of $11,463 to be received 7 years from today? Assume a discount rate of 3.5% compounded annually and rounded to the nearest $1.

$9,010

You won Texas State lottery of $25 million!!!! Texas Lottery Commission (TLC) promised you to pay $1 million every year for next 25 years. But you have been given another choice, a lump sum amount of $12.5 million today. How much is the interest rate that TLC is using? (Answer at the end)

. 6.24%

A rational investor would prefer to receive $ 1,200 today rather than $ 100 per month for 12 months.

True

You decide to borrow $250,000 to build a new home. The bank charges an interest rate of 8% compounded monthly. If you pay back the loan over 30 years, what will your monthly payments be (rounded to the nearest dollar)?

$1,834

Anna lent $20,000 to an attorney firm and was promised that she will be paid 6% annual return compounded continuously. If the business paid Anna the interest amount as well as the principal at the end of 5 years, how much in total did she get? If she had a choice of lending to a friend who would pay her 6% compounded weekly did she make a right choice by lending to the attorney firm rather than to her friend? Round it to the nearest 100

$27,000, Yes

You just invested $50,000 into an account that earns 7 percent compounded annually. At the beginning of each year you can withdraw $4,971. How many years can you continue to make the withdrawals (rounded to nearest year)?

16 (Hint: the payment is made at the beginning of the year)

Biff deposited $9,000 in a bank account, and 10yrs later he closes the bank account, which is worth $18000. What is the annual rate of interest has he earned over the years?

7.18%

When repaying an amortized loan, the interest payments increase over time due to the compounding process

False

Frank Zanca is considering three different investments that his broker has offered to him. The different cash flows are as follows: Because Frank only has enough savings for one investment, his broker has proposed the third alternative to be, according to his expertise, "the best in town." However, Frank questions his broker and wants to calculate the present value of each investment. Assuming a 15% discount rate, what is Frank's best alternative? (Answer at the end)

Investment A. $856.49 Investment B. $661.23 Investment C. $887.02 So, investment C is best.

You have two very similar investment options with same level of risks. Investment A brings in $5,000 every year for 7 years. Investment B brings in 56,000 in 7 years. What is the interest rate implicit in these two investment options?

More than 15%

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

$56,734

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

True

When solving a problem involving an annuity due. yon must select the "beg" or beginning mode on I your financial calculator

True

When using a financial calculator. cash outflows generally have to be entered as negative numbers, because a financial calculator sees money "leaving your hands."

True

A certificate of deposit that pays 9.8% compounded monthly is better than a similar certificate of deposit that pays 10% compounded only once per year

True (hint: compare the EAR)

A timeline identifies the timing and amount of a stream of cash flows, along with the interest rate it earns.

True

The future value of an annuity will increase if the interest rate goes up. but the present value of the I same annuity will decrease as the interest rate goes up

True

The present value of a deferred annuity (e.g., an annuity that starts 10 years from today) can be calculated in two steps: (1) calculate the present value of the annuity, and (2) calculate the present value of the amount determined in step (1).

True

The time value of money involves the opportunity cost of passing up the earning potential of a dollar today.

True

The present value of an annuity increases as the discount rate increases.

False

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

the current price of a $50 face value bond that matures in 10 years will be less than the current price of a $50 face value bond that matures on 5 years.

You have just purchased a share of preferred stock for $50.00. The preferred stock pays an annual dividend of $5.50 per share forever. What is the rate of return on your investment?

0.110

D'Anthony borrowed $50,000 today that he must repay in 15 annual end-of-year installments of $5,000. What annual interest rate is D'Anthony paying on his loan?

5.556%

Your grandparents deposit $2,000 each year on your birthday, starting the day you are born, in an account that pays 7% interest compounded annually. How much will you have in the account on your 21st birthday, just after your grandparents make their deposit?

$98,012

Charlie wants to retire in 15 years, and he wants to have an annuity of $50,000 a year for 20 years after retirement. Charlie wants to receive the first annuity payment the day he retires. Using an interest rate of 8%, how much must Charlie invest today in order to have his retirement annuity (round to nearest $10)?

$167,130

Today is your 20th birthday and your bank account balance is $25,000. Your account is earning 6.5% interest compounded semiannually. How much will be in the account on your 50th birthday?

$170,351 (Hint: adjust for N and I/Y)

Two sisters each open IRAs in 2011 and plan to invest $3,000 per year for the next 30 years. Mary makes her first deposit on January 1, 2011, and will make all future deposits on the first day of the year. Jane makes her first deposit on December 31, 2011, and will continue to make her annual deposits on the last day of each year. At the end of 30 years, the difference in the value of the IRAs (rounded to the nearest dollar), assuming an interest rate of 7% per year, will be

$19,837 (Hint: it is asking the difference in the future values of the two; BGN mode)

Your daughter is born today and you want her to be a millionaire by the time she is 35 years old. You open an investment account that promises to pay 12% per year. How much money must you deposit each year, starting on her 1st birthday and ending on her 35th birthday, so your daughter will have $1,000,000 by her 35th birthday?

$2,317

You plan to go to Asia to visit friends in three years. The trip is expected to cost a total of $10,000 at that time. Your parents have deposited $5,000 for you in a Certificate of Deposit paying 6% interest annually, maturing three years from now. Uncle Lee has agreed to pay for all remaining expenses. If you are going to put Uncle Lee's gift in an investment earning 10% over the next three years, how much must he deposit today, so you can visit your friends three years from today?

$3,039

Ryan borrowed $400,000 to buy a house; the annual interest rate is 5% and has a 25 year mortgage, paying monthly. It has been 7 years since he took the loan, and wants to refinance it. In order to do so, he first needs to know how much he still owes on the home so that he can pay that off and take a new loan (refinance) at the lower prevailing rate. How much does Ryan still owe to the bank?

$332,610

Manny and Irene will be retiring in fifteen years and would like to buy a Mexican villa. The villa costs $500,000 today,. and housing prices in Mexico are expected to increase by 6% per year. Manny and Irene want to make fifteen equal annual payments into an account. starting next year. so there will be enough money to purchase the villa in fifteen years. If the account earns 1076 per year, what is the amount of each deposit?

$37,714 (Hint: Step 1: first you want to know how much you need in 15 years- i.e., what the real estate price will grow to in 15 years for the given interest rate. Step 2: now that you know how much you want to have in 15 years (from step 1), you can find how much you want to deposit every year for a given interest rate)

Your parents are complaining about the price of items today compared to what they cost years ago. If an automobile that cost $12,000 in 1980 costs $42,000 in 2010, calculate the annual growth rate in the automobile's price.

$4.26%

Assume you are to receive a 10-year annuity with annual payments of $1000. The first payment will be received at the end of Year 1, and the last payment will be received at the end of Year 10. You will invest each payment in an account that pays 9 percent compounded annually. Although the annuity payments stop at the end of year 10, you will not withdraw any money from the account until 25 years from today, and the account will continue to earn 9% for the entire 25-year period. What will be the value in your account at the end of Year 25 (rounded to the nearest dollar)?

$55,340

The present value of $1,000 to be received in 5 yrs is ___ if the discount rate is 12.78%

$584

AutoLoans Corp. loans you $24,000 for four years to buy a car. The loan must be repaid in 48 equal monthly payments. The annual interest rate on the loan is 9 percent. What is the monthly payment?

$597.24

A financial advisor tells you that you can make your child a millionaire if you just start saving early. You decide to put an equal amount each year into an investment account that earns 7.5% interest per year, starting on the day your child is born. How much would you need to invest each year (rounded to the nearest dollar) to accumulate a million for your child by the time he/she is 35 years old? (Your last deposit will be made on his/her 34th birthday.)

$6,030 (Hint: since the parents are depositing the money on the day the child is born, it is 'beginning' payment [it would still be 'end' if the question said the parents deposited after the child turns one, see Q#25])

You estimate you'll need $200,000 per year for 25 years starting on your 65th birthday to live on during your retirement. Today is your 50th birthday and you want to make equal deposits into an account paying 9% interest per year, the first deposit today and the last deposit on your 64th birthday. How much must each deposit be (rounded to the nearest $10)?

$66,910 (BGN mode)

Jimmy just bought a new Ford SUV for his business. The price of the vehicle was $40,000. Jimmy made a $5,000 down payment and took out an amortized loan for the rest. The car dealership made the loan at 8% interest compounded monthly for five years. He is to pay back the principal and interest in equal monthly installments beginning one month from now. Determine the amount of Jimmy's monthly payment.

$709.67

An investment is expected to yield $300 in three years, $500 in five years, and $300 in seven years. What is the present value of this investment if our opportunity rate is 5%?

$864

You borrow $25,000 to be repaid in 12 monthly installments of $2,292.00. The annual interest rate is closest to

18%

At 6 percent compounded monthly, how long will it take to triple your money?

221 months (hint assume pv and fv, e.g., pv=-100 and fv=300 (3 times 100))

At what rate must $287.50 be compounded annually for it to grow to $650.01 in 14 years?

6%

You decide, you want to be a millionaire. You deposit S50,000 in an investment account that earns 9olo per year. The money in the account will be distributed to you whenever the total reaches $1,000,000. If you are 27 now, how old will you be when you get the money (rounded to the nearest year)? (Hint: to know how old you will be, you need to know for how long your money should be invested in)

62 yrs

You borrow $25,000 to buy a car, and agree to make 48 monthly payments of $607.39 to repay the loan. What annual rate of interest, which is being compounded monthly, are you being charged?

7.75%

I need your help! I have $15,000 that I can deposit in the Bank of Pandora and earn 4% interest rate compounded semi-annually or in the Bank of Titanic and earn 4% interest rate compounded continuously. If I can keep the deposit for 3 years, where should I deposit? By how much is this amount higher than if I deposited in the other bank?

Bank of Titanic, $20

Last National Bank is offering you a loan at 10%; payments on the loan are to be made monthly. Credit Onion is offering you a loan where payments are to be made semiannually; the rate on the loan is also 10%. Local Bank down the street is also offering a loan at 10% where the payments are made quarterly. Which loan has the lowest annual cost?

Credit Onion's loan (hint: we are looking at cost i.e., cost for the bank and not returns for the investor)

$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).

False

An investment earning simple interest is preferred over an investment earning compound interest because the simplicity adds value.

False

John has to pay $1,000 per month for his mortgage for another 5 years. but he is considering paying the mortgage off in one lump sum. John cannot calculate the present value of tire payments using the annuity formulas because his payments are monthly and not once per year

False

You can buy a $50 savings bond today for $25 and redeem the bond in 10 years for its full face value of $50. You could also put your money in a money market account that pays 7% interest per year. Which option is better, assuming they are of equal risk?

The savings bond is better because it earns a higher interest rate. (Hint: the first option has all the information other than the interest rate, which you can compute, and then compare it with the interest rate on the money market investment)

Artificially low interest rates helped create the housing bubble because low interest rates (r value) create higher values (higher PVs).

True

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

True

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

True

If the interest rate is positive, then the future value of an annuity due will be greater than the future value of an ordinary annuity.

True

If we invest money for 10 years at 8 percent interest, compounded semiannually, we are really investing money for 20 six-month periods, and receiving 4 percent interest each period.

True

If you only earned interest on your initial investment and not on previously earned interest it would be called simple interest

True

The future value of an annuity due is greater than the future value of an otherwise identical ordinary annuity

True

The present value of a single future sum of money is inversely related to both the number of years until I payment is received and the discount rate.

True

The value of a bond investment, which provides fixed interest payments, will increase when I discounted at an 8%o r ate rather than at an 1% rale.

True

Tim has $100 in a bank account paying 2o/o interest per year. At the end of 5 years, Tim's bank account balance will be $ll0 if interest is not compounded. but will be greater than $l l0 if interest is compounded.

True

Which of the following investments has the highest effective annual return (EAR)? (Assume that all CDs are of equal risk.)

a bank CD that pays 7.25 percent compounded semiannually (Hint: first calculate EAR for each)

What is the present value of the following perpetuities? a. $200 per year discounted at 6% annually b. $500 per year discounted at 9% annually

a. $3,333.33 b.$5,555.56

You have the choice of two equally risky annuities, each paying $5,000 per year for 8 years. One is an annuity due and the other is an ordinary annuity. If you are going to be receiving the annuity payments, which annuity would you choose to maximize your wealth?

the annuity due (Idea: depositing money earlier, i.e., in the beginning (annuity due) earns your more interest)