Quiz 2: Time Value of Money
Business
Q 1Q 1
What is the amount of interest earned on $2,000 for five years at 6% simple interest per year?
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Essay
Given information:
• Amount deposited is $2,000.
• At simple interest rate of 6 percent.
• Time period for withdrawal is 5 year.
The total amount of interest earned from present deposit:
The total amount of interest earned from present deposit can be calculated by using the following formula: 
…… (1)Where,
I = Total amount of interest rate earned
P = Present value
N = Number of years
i = Rate of interest
Substitute the respective values in Equation (1), to obtain the total amount of interest earned from the present deposit. 
Hence, the total amount of interest earned from the present deposit is 
.
Q 2Q 2
You wish to have $10,000 in an account 10 years from now. How much money must be deposited in the account now in order to have this amount if the account pays 8% compounded annually? (a) $1,490
(b) $3,871
(c) $4,632
(d) $5,584
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Multiple Choice
Given information:
An account cash balance after 10 years at 8 percent compound interest rate is expected to be $10,000.
The present equivalent worth of the future cash flow:
The present equivalent worth of the future cash flow can be calculated by using the following formula: 
…… (1)Where,
P = Present value
F = Future worth value
N = Number of years
i = Rate of interest
Substitute the respective values in Equation (1) to obtain the amount of money to be deposited in the account at current period. 
Since the present equivalent worth of deposited amount is 
, option (b) is selected.
Q 3Q 3
You deposit $3,000 in a savings account that earns 8% simple interest per year. How many years will it take to double your balance? If, instead, you deposit the $3,000 in another savings account that earns 7% interest compounded yearly, how many years will it take to double your balance?
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Essay
The given information:
Deposit amount is $3,000
Simple interest rate is 8%
Interest rate compounded annually is 7%
Formula:
Future value:
Simple interest rate is represented as follows: 
…… (1)Future value formula by using interest rate compounded annually is represented as follows: 
Here,
i = Interest rate
n = Number of years
Time taken to double the balance:
i = 8%
P = 3,000
Substitute the given values in equation (1) to get the time period to double the balance this can be calculated as follows: 
Thus, the number of years to double the investment at 8 percent simple interest rate is 
Time taken by present worth of savings to double:
i = 7% compounded annually
P = 3,000
Substitute the given values in equation (2) to get the time period to double the balance this can be calculated as follows: 
Taking log on both sides to get the value of t, 
Thus, the number of years to double the investment at 7% interest compounded annually is 
Q 4Q 4
Assume that $500 is deposited today, two years from now, four years from now, six years from now, and eight years from now. At a 10% interest compounded annually, determine the future value at the end of year 9.
(a) $4,174
(b) $3,790
(c) $2,085
(d) $1,895
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Multiple Choice
Q 5Q 5
Compare the interest earned on $15,000 for 25 years at 7% simple interest with the amount of interest earned if interest were compounded annually.
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Q 6Q 6
What single payment at the end of year 5 is equivalent to an equal annual series of payments of $800 beginning at the end of year 3 and ending at the end of year 12? The interest rate is 8% compounded annually. (a) $5,797
(b) $6,260
(c) $6,762
(d) $6,883
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Multiple Choice
Q 7Q 7
Bank A pays 6% simple interest on its savings account balances. Bank B pays 5.5% interest compounded annually. If you made a $10,000 deposit in each bank, which bank provides you more money at the end of 15 years?
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Essay
Q 8Q 8
Four years ago, you opened a mutual fund account and made three deposits ($200 four years ago, $X three years ago, and $300 a year ago) where you earned varying interest rates according to the following diagram. Today, your balance shows $1,000. Determine the amount of deposit that was made three years ago ($X). See the following figure. (a) $215
(b) $237
(c) $244
(d) $259
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Multiple Choice
Q 9Q 9
You are considering investing $1,000 at an interest rate of 6.5% compounded annually for five years or investing the $1,000 at 6.8% per year simple interest for five years. Which option is better?
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Q 10Q 10
How much money should be deposited now in an account that pays 10% interest compounded annually in order to make five equal annual withdrawals of $5,000? (a) $8,052
(b) $9,050
(c) $16,761
(d) $18,954
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Multiple Choice
Q 11Q 11
You are about to borrow $10,000 from a bank at an interest rate of 9% compounded annually. You are required to make five equal annual repayments in the amount of $2,570.92 per year, with the first repayment occurring at the end of year 1. For each year, show the interest payment and principal payment.
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Q 12Q 12
What value of C makes these two cash flows equivalent at an interest rate of 10%?
(a) $29.65
(b) $35.98
(c) $47.33
(d) $43.96
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Multiple Choice
Q 13Q 13
Suppose you have the alternative of receiving either $5,000 at the end of five years or P dollars today. Currently, you have no need for the money, so you could deposit the P dollars into a bank account that pays 7% interest compounded annually. What value of P would make you indifferent in your choice between P dollars today and the promise of $5,000 at the end of five years?
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Q 14Q 14
Calculate the future worth of 20 annual $2,000 deposits in a savings account that earns 9% (compounded annually). Assume that all deposits are made at the beginning of each year. (a) $126,005
(b) $111,529
(c) $113,529
(d) $92,037
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Multiple Choice
Q 15Q 15
Suppose that, to cover some of your college expenses, you are obtaining a personal loan from your uncle in the amount of $25,000 (now) to be repaid in two years. If your uncle could earn 8% interest (compounded annually) on his money invested in various sources, what minimum lump-sum payment two years from now would make your uncle happy economically?
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Q 16Q 16
You borrow $20,000 from a bank to be repaid in three equal annual installments at 9% interest compounded annually. What is the portion of interest payment for the second annual payment? (a) $1,800
(b) $1,251
(c) $1,089
(d) $549
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Multiple Choice
Q 17Q 17
Which of the following alternatives would you choose, assuming an interest rate of 10% compounded annually?
Alternative 1: Receive $100 today.
Alternative 2: Receive $120 two years from now.
Alternative 3: Receive $170 five years from now.
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Essay
Q 18Q 18
The following two cash flows are said to be economically equivalent at 10% interest. Determine the value of X for the second cash flow series.
(a) X = $1,505
(b) X = $1,500
(c) X = $1,197
(d) X = $1,192
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Multiple Choice
Q 19Q 19
Today you deposited $1,000 in a savings account paying 5% annual interest. How much should you have at the end of three years?
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Q 20Q 20
What is the amount of five equal annual deposits that can provide five annual withdrawals, where a first withdrawal of $1,000 is made at the end of year 6 and subsequent withdrawals increase at the rate of 10% year over the previous year's if the interest rate is 10% compounded annually? (a) $745
(b) $789
(c) $1,000
(d) $1,563
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Multiple Choice
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Q 22Q 22
You borrowed $4,000 to finance your educational expenses at the beginning of your junior year of college at an interest rate of 9% compounded annually. You are required to pay off the loan with five equal annual installments, but the first payment will be deferred until your graduation. Determine the value of C, the amount of annual payments.
(a) C = $891
(b) C = $1,082
(c) C = $1,121
(d) C = $1,222
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Multiple Choice
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Q 24Q 24
Consider the following cash flow series at varying interest rates. What is the equivalent present worth of the cash flow series?
(a) P = $5,068
(b) P = $4,442
(c) P = $4,077
(d) P = $3,833
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Multiple Choice
Q 25Q 25
State the amount accumulated by each of the following present investments:
(a) $6,000 in 8 years at 6% compounded annually.
(b) $1,550 in 12 years at 5% compounded annually.
(c) $8,000 in 32 years at 9% compounded annually.
(d) $12,000 in 9 years at 8% compounded annually.
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Q 26Q 26
At what annual interest rate will $1,000 invested today be worth $2,000 in 10 years? (a) 6.5%
(b) 7.2%
(c) 9.3%
(d) 5.8%
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Multiple Choice
Q 27Q 27
State the present worth of the following future payments:
(a) $5,500 six years from now at 10% compounded annually.
(b) $7,000 three years from now at 9% compounded annually.
(c) $22,000 five years from now at 8% compounded annually.
(d) $13,000 eight years from now at 7% compounded annually.
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Q 28Q 28
If you borrow $20,000 at an interest rate of 8%, compounded annually, with the repayment schedule as shown, what is the amount A ? (Note that there is a missing payment in year 5.)
(a) A = $2,393
(b) A = $2,793
(c) A = $3,193
(d) A = $3,593
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Multiple Choice
Q 29Q 29
Assuming an interest rate of 8% compounded annually, answer the following questions:
(a) How much money can be loaned now if $8,000 is to be repaid at the end of five years?
(b) How much money will be required in four years in order to repay a $10,000 loan borrowed now?
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Essay
Q 30Q 30
You plan to make 15 annual deposits in a saving account that pays 6% interest compounded annually. If the first deposit of $1,000 is made at the end of the first year and each subsequent deposit is $500 more than the previous one, the value of the account at the end of 15 years will be nearly: (a) $87,021
(b) $92,242
(c) $97,777
(d) $71,550
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Multiple Choice
Q 31Q 31
How many years will it take an investment to triple if the interest rate is 7% compounded annually?
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Q 32Q 32
How long would it take an investment to triple if the interest rate is 8% compounded annually? (a) 9 years
(b) 12 years
(c) 14 years
(d) 16 years
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Multiple Choice
Q 33Q 33
How many years will it take to double your investment of $2,000 if it has an interest rate of 6% compounded annually?
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Q 34Q 34
If you borrow $25,000 at an interest rate of 9%, compounded annually with the following repayment schedule, what is the required amount A?
(a) A = $5,576
(b) A = $8,883
(c) A = $9,521
(d) A = $8,014
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Multiple Choice
Q 35Q 35
You bought 100 shares of GE stock at $2,330 on December 31, 2011. Your intention is to keep the stock until it doubles in value. If you expect 8% annual growth for GE stock, how many years do you expect to hold onto the stock? Compare your answer with the solution obtained by the Rule of 72 (discussed in Example 2.7).
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Q 36Q 36
If $1,000 is deposited in a savings account at the beginning of each year for 20 years (a total number of deposits = 20) and the account draws interest at 7% compounded annually, the value of the account at the end of 20 years will be nearly: (a) $21,400
(b) $46,936
(c) $40,996
(d) $43,865
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Multiple Choice
Q 37Q 37
In 1626 the Indians sold Manhattan Island to Peter Minuit of the Dutch West Company for $24. If they saved just $1 from the proceeds in a bank account that paid an 8% annual interest, how much would their descendents have in 2015?
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Q 38Q 38
If you want to withdraw $10,000 at the end of two years and $35,000 at the end of four years, how much should you deposit now into an account that pays 9% interest compounded annually? See the accompanying cash flow diagram.
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Q 39Q 39
You are interested in buying a piece of real estate property that could be worth $450,000 in five years. If your earning interest rate is 5%, how much would you be willing to pay for this property now?
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Q 40Q 40
John and Susan just opened savings accounts at two different banks. Each deposited $1,000. John's bank pays simple interest at an annual rate of 10%, whereas Susan's bank pays compound interest at an annual rate of 9.5%. No principal or interest will be taken out of the accounts for a period of five years. At the end of five years, whose balance will be higher and by how much (to the nearest dollar)?
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Q 41Q 41
A project is expected to generate a cash flow of $2,000 in year 1, $800 in year 2, and $1,000 in year 3. At an interest rate of 10%, what is the maximum amount that you could invest in the project at year 0?
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Q 42Q 42
If you desire to withdraw the given amounts over the next five years from a savings account that earns 5% interest compounded annually, how much do you need to deposit now?
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Q 43Q 43
If $2,000 is invested now, $3,000 two years from now, and $4,000 four years from now at an interest rate of 8% compounded annually, what will be the total amount in 10 years?
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Q 44Q 44
A local newspaper headline blared, "Bo Smith Signs for $30 Million." The article revealed that Bo Smith, the former record-breaking running back from Football University, signed a $30 million package with the Nebraska Lions. The terms of the contract were $3 million immediately, $2.4 million per year for the first five years (with the first payment after one year), and $3 million per year for the next five years (with the first payment at the end of year 6). If the interest rate is 8% compounded annually, what is Bo's contract worth at the time of contract signing?
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Q 45Q 45
How much invested now at an interest rate of 9% compounded annually would be just sufficient to provide three payments as follows: the first payment in the amount of $3,000 occurring two years from now, the second payment in the amount of $4,000 five years thereafter, and the third payment in the amount of $5,000 seven years thereafter?
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Q 46Q 46
You deposit $2,000 today, $3,000 one year from now, and $5,000 three years from now. How much money will you have at the end of year 3 if there are different annual compound-interest rates per period, according to the accompanying diagram?
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Q 47Q 47
A company borrowed $180,000 at an interest rate of 9% compounded annually over six years. The loan will be repaid in installments at the end of each year according to the accompanying repayment schedule. What will be the size of the last payment (X) that will pay off the loan?
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Q 48Q 48
You are preparing to buy a vacation home five years from now. The home will cost $80,000 at that time. You plan on saving three deposits at an interest rate of 8%:
Deposit 1: Deposit $10,000 today.
Deposit 2: Deposit $12,000 two years from now.
Deposit 3: Deposit $ X three years from now.
How much do you need to invest in year 3 to ensure that you have the necessary funds to buy the vacation home at the end of year 5?
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Q 49Q 49
The accompanying diagram shows the anticipated cash dividends for Delta Electronics over the next four years. John is interested in buying some shares of this stock for a total of $100 and will hold them for four years. If John's interest rate is known to be 8% compounded annually, what would be the desired (minimum) total selling price for the set of shares at the end of the fourth year?
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Q 50Q 50
You are considering purchasing a machine that is expected to produce the following cash flows: $60,000 in year 1, $77,000 in year 2, $65,000 in year 3, $57,000 in year 4, and $45,000 in year 5. If your interest rate is 14%, what would be your maximum offer (purchase price) on this machine?
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Q 51Q 51
You are planning to contribute $5,000 a year to a mutual fund that earns an average of 6% per year. If you continue to contribute for the next 10 years, how much would you have in your account?
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Q 52Q 52
What is the future worth of a series of equal yearly deposits of $5,000 for 7 years in a savings account that earns 5% annual compound interest if
(a) all deposits are made at the end of each year?
(b) all deposits are made at the beginning of each year?
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Q 53Q 53
What is the future worth of each given series of payments?
(a) $6,000 at the end of each year for six years at 6% compounded annually.
(b) $8,000 at the end of each year for nine years at 7.25% compounded annually.
(c) $15,000 at the end of each year for 25 years at 8% compounded annually.
(d) $3,000 at the end of each year for 10 years at 9.75% compounded annually.
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Q 54Q 54
What equal annual series of payments must be paid into a sinking fund in order to accumulate each of the following given amounts?
(a) $18,000 in 13 years at 5% compounded annually.
(b) $11,000 in eight years at 6% compounded annually.
(c) $8,000 in 25 years at 8% compounded annually.
(d) $12,000 in eight years at 6.85% compounded annually.
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Q 55Q 55
Your company wants to set aside a fixed amount every year to a sinking fund to replace a piece of industrial equipment costing $250,000 at the end of five years from now. The sinking fund is expected to earn 5% interest. How much must your company deposit each year to meet this goal?
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Q 56Q 56
You want to save the down payment required to purchase a vacation home at the end of five years. If the required down payment is $25,000 and you can earn 5% a year on your savings account, how much do you need to set aside at the end of each of the next five years?
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Q 57Q 57
Part of the income that a machine generates is put into a sinking fund to pay for its replacement when it wears out. If $3,000 is deposited every year at 6% interest compounded annually, how many years must the machine be kept before a new machine costing $35,000 can be purchased?
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Q 58Q 58
A no-load (commission-free) mutual fund has grown at a rate of 9% compounded annually since its beginning. If it is anticipated that it will continue to grow at this rate, how much must be invested every year so that $10,000 will be accumulated at the end of five years?
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Q 59Q 59
You open a bank account, making a deposit of $500 now and deposits of $1,000 every other year. What is the total balance at the end of 10 years from now if your deposits earn 4% interest compounded annually?
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Q 60Q 60
What equal-annual-payment series is required in order to repay each of the following given present amounts?
(a) $18,000 in five years at 8% interest compounded annually.
(b) $4,200 in four years at 9.5% interest compounded annually.
(c) $7,700 in three years at 11% interest compounded annually.
(d) $23,000 in 20 years at 6% interest compounded annually.
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Q 61Q 61
You have borrowed $20,000 at an interest rate of 10% compounded annually. Equal payments will be made over a three-year period with each payment made at the end of the corresponding year. What is the amount of the annual payment? What is the interest payment for the second year?
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Q 62Q 62
What is the present worth of each of the following given series of payments?
(a) $9,000 at the end of each year for eight years at 6% compounded annually.
(b) $1,500 at the end of each year for 10 years at 9% compounded annually.
(c) $7,500 at the end of each year for six years at 7.25% compounded annually.
(d) $5,000 at the end of each year for 30 years at 8.75% compounded annually.
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Q 63Q 63
From the interest tables in Appendix B, determine the value of the following factors by interpolation, and compare the results with those obtained from evaluating the A/P and P/A interest formulas:
(a) The capital-recovery factor for 36 periods at 6.25% compound interest.
(b) The equal-payment-series present-worth factor for 125 periods at 9.25% compound interest.
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Q 64Q 64
If $500 is deposited in a savings account at the beginning of each year for 15 years and the account earns 7% interest compounded annually, what will be the balance on the account the end of the 15 years (F)?
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Q 65Q 65
If you borrow $5,000 and agree to repay the loan in five equal annual payments at an interest rate of 11%, what will the annual payment be? What if you make the first payment on the loan at the end of second year?
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Q 66Q 66
A company is considering replacing an old piece of industrial equipment to reduce operating and maintenance cost. A new equipment is quoted at $195,000. After 10 years, the machine would have no value, but it would save as much as $30,000 in operating and maintenance cost. If the firm's interest rate is 10%, is it worth buying the new equipment?
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Q 67Q 67
An investment costs $3,460 and pays $250 in perpetuity. What is the interest earned on this investment?
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Q 68Q 68
At an interest rate of 10%, what is the present value of an asset that produces $1,000 a year in perpetuity?
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Q 69Q 69
Kim deposits her annual bonus into a savings account that pays 8% interest compounded annually. The size of her bonus increases by $2,000 each year, and the initial bonus amount is $5,000. Determine how much will be in the account immediately after the fifth deposit.
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Q 70Q 70
Five annual deposits in the amounts of $5,000, $4,500, $4,000, $3,500, and $3,000 are made into a fund that pays interest at a rate of 10% compounded annually. Determine the amount in the fund immediately after the fifth deposit.
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Q 72Q 72
What is the equal-payment series for 10 years that is equivalent to a payment series starting with $30,000 at the end of the first year and decreasing by $3,000 each year over 10 years? Interest is 8% compounded annually.
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Q 73Q 73
The maintenance expense on a machine is expected to be $3,000 during the first year and to increase $600 each year for the following eight years. What present sum of money should be set aside now to pay for the required maintenance expenses over the eight-year period? (Assume 12% compound interest per year.)
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Q 74Q 74
Consider the cash flow series given in the accompanying table. What value of C makes the deposit series equivalent to the withdrawal series at an interest rate of 9% compounded annually?
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Q 75Q 75
Matt Christopher is a 25-year-old mechanical engineer, and his salary next year will be $60,000. Matt expects that his salary will increase at a steady rate of 5% per year until his retirement at age 65. If he saves 10% of his salary each year and invest these savings at an interest rate of 9%, how much will he have at his retirement?
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Q 76Q 76
Suppose that an oil well is expected to produce 100,000 barrels of oil during its first production year. However, its subsequent production (yield) is expected to decrease by 10% over the previous year's production. The oil well has a proven reserve of 1,000,000 barrels.
(a) Suppose that the price of oil is expected to be $100 per barrel for the next seven years. What would be the present worth of the anticipated revenue stream at an interest rate of 12% compounded annually over the next seven years?
(b) Suppose that the price of oil is expected to start at $100 per barrel during the first year, but to increase at the rate of 5% over the previous year's price. What would be the present worth of the anticipated revenue stream at an interest rate of 12% compounded annually over the next seven years?
(c) Assume the conditions of part (b). After three years of production, you decide to sell the oil well. What would be the fair price for the oil well based on four more years of production?
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Q 77Q 77
A city engineer has estimated the annual toll revenues from a proposed highway construction project over 20 years as follows:
A n = ($2,000,000)(n)(1.06) n-1
n = 1, 2,... , 20.
To determine the amount of debt financing through bonds, the engineer was asked to present the estimated total present value of toll revenue at an interest rate of 6%. Assuming annual compounding, find the present value of the estimated toll revenue.
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Q 78Q 78
What is the amount of 10 equal annual deposits that can provide five annual withdrawals, when a first withdrawal of $3,000 is made at the end of year 11 and subsequent withdrawals increase at the rate of 6% per year over the previous year's rate if
(a) the interest rate is 8% compounded annually?
(b) the interest rate is 6% compounded annually?
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Q 79Q 79
You are planning to save $1 million for retirement over the next 30 years.
(a) If you are earning interest at the rate of 6% and you live 20 years after retirement, what annual level of living expenses will those savings support?
(b) Suppose your retirement living expenses will increase at an annual rate of 3% due to inflation. Determine the annual spending plan in line with your inflation.
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Q 81Q 81
Find the present worth of the cash receipts in the accompanying diagram if i = 10% compounded annually with only four interest factors.
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Q 82Q 82
In computing the equivalent present worth of the cash flow series at period 0, which of the following expressions is incorrect? (a) P = $100(P/A, i, 4)(P/F, i, 4).
(b) P = $100(F/A, i, 4)(P/F, i, 7).
(c) P = $100(P/A, i, 7) - $100(P/A, i, 3).
(d) P = $100[(P/F, i, 4) + (P/F, i, 5) + (P/F, i, 6) + (P/F, i, 7)].
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Multiple Choice
Q 83Q 83
Find the equivalent present worth of the cash receipts in the accompanying diagram, where i = 10% compounded annually. In other words, how much do you have to deposit now (with the second deposit in the amount of $500 at the end of the first year) so that you will be able to withdraw $300 at the end of the second year through the fourth year, and $800 at the end of the fifth year if the bank pays you 10% annual interest on your balance?
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Q 84Q 84
What value of A makes the two annual cash flows shown in the following diagram equivalent at 10% interest compounded annually?
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Q 85Q 85
The two cash flow transactions shown in the accompanying cash flow diagram are said to be equivalent at 10% interest compounded annually. Find the unknown X value that satisfies the equivalence.
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Q 86Q 86
State the value of C that makes the following two cash flow transactions economically equivalent at an interest rate of 10%:
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Q 87Q 87
From the following cash flow diagram, find the value of C that will establish economic equivalence between the deposit series and the withdrawal series at an interest rate of 9% compounded annually.
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Q 88Q 88
The following equation describes the conversion of a cash flow into an equivalent equal-payment series with N = 10:
A = [800 + 20(A/G, 6%, 7)]
* (P/A, 6%, 7)(A/P, 6%, 10)
+ [300(F/A, 6%, 3) - 500](A/F, 6%, 10).
Given the equation, reconstruct the original cash flow diagram.
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Q 89Q 89
Consider the following cash flow diagram. What value of C makes the inflow series equivalent to the outflow series at an interest rate of 12% compounded annually?
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Q 90Q 90
Four years ago, you opened a mutual fund account and made three deposits ($200 four years ago, $ X three years ago, and $300 a year ago) where you earned varying interest rates according to the diagram that follows. Today your balance shows $1,000. Determine the amount of the deposit made three years ago ($X).
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Q 91Q 91
A father decides to establish a savings account for his child's college education on the day his baby is born. Any money put into the account will earn an interest rate of 8% compounded annually. The father will make a series of annual deposits in equal amounts from the 1st birthday through the 18th birthday so that the child can make four annual withdrawals from the account in the amount of $20,000 on each of his 18th, 19th, 20th, and 21st birthdays. Assuming that the first withdrawal will be made on the child's 18th birthday, calculate the required annual deposit A.
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Q 92Q 92
Find the value of X such that the following two cash flow transactions are economically equivalent at 10% compounded annually.
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Q 93Q 93
What single payment at the end of year 5 is equivalent to an equal annual series of payments of $800 beginning at the end of year 3 and ending at the end of year 12? The interest rate is 8% compounded annually.
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Q 94Q 94
You borrowed $4,000 to finance your educational expenses at the beginning of your junior year of college at an interest rate of 9% compounded annually. You are required to pay off the loan with five equal annual installments, but the first payment will be deferred until your graduation. Determine the value of C, the amount of annual payments.
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Q 95Q 95
Consider the following cash flow series at varying interest rates. What is the equivalent present worth of the cash flow series?
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Q 96Q 96
It is said that a lump-sum amount of $50,000 at the end of five years is equivalent to an equal-payment series of $5,000 per year for 10 years, where the first payment occurs at the end of year 1. What earning interest is assumed in this calculation?
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Q 97Q 97
At what rate of interest compounded annually will an investment double in five years? Find the answers by using (1) the exact formula and (2) the Rule of 72.
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Q 98Q 98
Determine the interest rate i that makes the pairs of cash flows shown in the following diagrams economically equivalent.
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Q 99Q 99
You have $10,000 available for investment in stock. You are looking for a growth stock that can grow your investment to $35,000 over five years. What kind of growth rate are you looking for?
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Q 100Q 100
Recently, a suburban Chicago couple won Powerball, a multistate lottery game. The game had rolled over for several weeks, so a huge jackpot was at stake. Ticket buyers had the choice between a single lump sum of $104 million or a total of $198 million paid out over 25 years (or $7.92 million per year and the payment is made immediately) should they win the game. The winning couple opted for the lump sum. At what interest rate will these two payment options be equivalent?
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Q 101Q 101
The state of Florida sold a total of $36.1 million worth of lottery tickets at $1 each during the first week of January 2011. As prize money, a total of $41 million will be distributed over the next 21 years ($1,952,381 at the beginning of each year). The distribution of the first-year prize money occurs now, and the remaining lottery proceeds are put into the state's educational reserve funds, which earn interest at the rate of 6% compounded annually. After the last prize distribution has been made (at the beginning of year 21), how much will be left in the reserve account?
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Q 102Q 102
A newspaper headline reads, "Millionaire Babies: How to Save Our Social Security System." It sounds a little wild, but the concept expressed in the title of this newspaper headline probably refers to an economic plan proposed by a member of Congress. Senator Bob Kerrey (D-Nebraska) has proposed giving every newborn baby a $1,000 government savings account at birth, followed by five annual contributions of $500 each. (Kerrey offered this idea in a speech devoted to tackling Social Security reform.) If the funds are left untouched in an investment account, Kerrey says, then by the time each baby reaches age 65, his or her $3,500 contribution will have grown to $600,000 over the years, even at medium returns for a thrift-savings plan. At about 9.4% compounded annually, the balance would grow to be $1,005,132. (How would you calculate this number?) Since about 4 million babies are born each year, the proposal would cost the federal government $4 billion annually. About 90% of the total annual Social Security tax collections of more than $300 billion is used to pay current beneficiaries, making Social Security one of the largest federal programs in dollar expenditure. The remaining 10% is invested in interest-bearing government bonds that finance the day-to-day expenses of the federal government. Discuss the economics of Senator Bob Kerrey's Social Security savings plan.
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Q 103Q 103
In 2011, Kevin Jones, Texas Tigers quarterback, agreed to an eight-year, $50 million contract that at the time made him the highest-paid player in professional football history. The contract included a signing bonus of $11 million and called for annual salaries of $2.5 million in 2011, $1.75 million in 2012, $4.15 million in 2013, $4.90 million in 2014, $5.25 million in 2015, $6.2 million in 2016, $6.75 million in 2017, and $7.5 million in 2018. The $11 million signing bonus was prorated over the course of the contract so that an additional $1.375 million was paid each year over the eight-year contract period. With the salary paid at the beginning of each season, what is the worth of his contract at an interest rate of 6%?
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