Question 1

Skyline Industries will need $1.8 million 5 years from now to replace some equipment.Currently,the firm has some extra cash and would like to establish a savings account for this purpose.The account pays 5.25 percent interest,compounded annually.How much money must the company deposit today to fully fund the equipment purchase?
A)$1,279,947.20
B)$1,298,407.21
C)$1,350,868.47
D)$1,393,676.52
E)$1,412,308.18

Accepted Answer

Present value = $1,800,000/(1 + 0.0525)⁵ = $1,393,676.52

Question 2

Sixty years ago,your grandparents opened two savings accounts and deposited $200 in each account.The first account was with City Bank at 3 percent,compounded annually.The second account was with Country Bank at 3.5 percent,compounded annually.Which one of the following statements is true concerning these accounts?
A)The City Bank account is currently worth $1,201.54.
B)The City Bank account has earned $211.19 more in interest than the Country Bank account.
C)The Country Bank account is currently worth $1,526.08.
D)The Country Bank account has paid $367.48 more in interest than the City Bank account.
E)The Country Bank account has paid $397.30 more in interest than the City Bank account.

Accepted Answer

Future value _{City Bank} = $200 × (1 + 0.03)⁶⁰ = $1,178.32Future value _{Country Bank} = $200 × (1 + 0.035)⁶⁰ = $1,575.62Difference = $1,575.62 - $1,178.32 = $397.30

Question 3

You want to have $25,000 for a down payment on a house 6 years from now.If you can earn 6.5 percent,compounded annually,on your savings,how much do you need to deposit today to reach your goal?
A)$17,133.35
B)$17,420.73
C)$17,880.69
D)$18,211.17
E)$18,886.40

Accepted Answer

Present value = $25,000/(1 + 0.065)⁶ = $17,133.35

Question 4

Your coin collection contains ten 1939 silver dollars.If your great grandparents purchased them for their face value when they were new,how much will your collection be worth when you retire in 2050,assuming they appreciate at a 5.1 percent annual rate?
A)$2,243.63
B)$2,329.29
C)$2,348.98
D)$2,499.78
E)$2,644.29

Accepted Answer

Future value = $10 × (1 + 0.051)^{(2050 - 1939)} = $2,499.78

Question 5

Your friend claims that he invested $5,000 seven years ago and that this investment is worth $38,700 today.For this to be true,what annual rate of return did he have to earn? Assume the interest compounds annually.
A)28.87 percent
B)31.39 percent
C)33.96 percent
D)36.01 percent
E)37.87 percent

Accepted Answer

$38,700 = $5,000 × (1 + r)⁷; r = 33.96 percent

Question 6

Ten years from now,you will be inheriting $100,000.What is this inheritance worth to you today if you can earn 5.5 percent interest,compounded annually?
A)$58,543.06
B)$63,215.46
C)$72,419.05
D)$72,798.47
E)$74,003.15

Accepted Answer

Present value = $100,000/(1 + 0.055)¹⁰ = $58,543.06

Question 7

At 10 percent interest,how long does it take to quadruple your money?
A)14.33 years
B)14.55 years
C)15.11 years
D)15.36 years
E)15.56 years

Accepted Answer

$4 = $1 × (1 + 0.10)^t; t = 14.55 years

Question 8

You have been told that you need $25,600 today in order to have $100,000 when you retire 35 years from now.What rate of interest was used in the present value computation? Assume interest is compounded annually.
A)3.97 percent
B)4.15 percent
C)4.29 percent
D)4.53 percent
E)4.58 percent

Accepted Answer

$100,000 = $25,600 × (1 + r)³⁵; r = 3.97 percent

Question 9

You want to have $45,000 in cash to buy a car 4 years from today.You expect to earn 4.5 percent,compounded annually,on your savings.How much do you need to deposit today if this is the only money you save for this purpose?
A)$33,618.92
B)$34,511.68
C)$35,726.04
D)$37,735.26
E)$38,156.19

Accepted Answer

Present value = $45,000/(1 + 0.045)⁴ = $37,735.26

Question 10

Today,Stacy is investing $26,000 at 6.0 percent,compounded annually,for 4 years.How much additional income could he earn if he had invested this amount at 7 percent,compounded annually?
A)$1,043.11
B)$1,256.30
C)$1,401.16
D)$1,442.79
E)$1,484.08

Accepted Answer

Future value _6.0% = $26,000 × (1 + 0.060)⁴ = $32,824.40Future value _7% = $26,000 × (1 + 0.07)⁴ = $34,080.70Difference = $34,080.70 - $32,824.40 = $1,256.30

Question 11

Isaac only has $690 today but needs $800 to buy a new laptop.How long will he have to wait to buy the laptop if he earns 5.4 percent compounded annually on his savings?
A)2.29 years
B)2.48 years
C)2.51 years
D)2.77 years
E)2.81 years

Accepted Answer

$800 = $690 × (1 + 0.054)^t; t = 2.81 years

Question 12

You have $1,100 today and want to triple your money in 5 years.What interest rate must you earn if the interest is compounded annually?
A)18.08 percent
B)19.90 percent
C)22.15 percent
D)24.57 percent
E)27.21 percent

Accepted Answer

$3,300 = $1,100 × (1 + r)⁵; r = 24.57 percent

Question 13

You're trying to save to buy a new $210,000 Ferrari.You have $38,000 today that can be invested at your bank.The bank pays 4.1 percent annual interest on its accounts.How long will it be before you have enough to buy the car?
A)39.13 years
B)39.29 years
C)40.67 years
D)41.08 years
E)42.54 years

Accepted Answer

$210,000 = $38,000 × (1 + 0.041)^t; t = 42.54 years

Question 14

Planters Bank pays 5 percent simple interest on its savings account balances,whereas Centura Bank pays 5 percent compounded annually.If you made a $12,000 deposit in each bank,how much more money would you earn from your Centura Bank account at the end of 20 years?
A)$7,155.84
B)$7,839.57
C)$7,960.47
D)$8,400.09
E)$8,784.14

Accepted Answer

Future value _Planters = $12,000 + ($12,000 × 0.05 × 20) = $24,000Future value _{Centura Street} = $12,000 × (1 + 0.05)²⁰ = $31,839.57Difference = $31,839.57 - $24,000 = $7,839.57

Question 15

You have $1,500 today in your savings account.How long must you wait for your savings to be worth $4,000 if you are earning 1.1 percent interest,compounded annually?
A)76.68 years
B)79.69 years
C)72.13 years
D)80.57 years
E)89.66 years

Accepted Answer

$4,000 = $1,500 × (1 + 0.011)^t; t = 89.66years

Question 16

How long will it take to double your savings if you earn 7.2 percent interest,compounded annually?
A)8.89 years
B)9.02 years
C)9.34 years
D)9.97 years
E)11 years

Accepted Answer

$2 = $1 × (1 + 0.072)^t; t = 9.97 years

Question 17

You and your sister are planning a large anniversary party 3 years from today for your parents' 50^th wedding anniversary.You have estimated that you will need $4,500 for this party.You can earn 2.5 percent compounded annually on your savings.How much would you and your sister have to deposit today in one lump sum to pay for the entire party? A)$4,076.55 B)$4,178.70 C)$4,308.16 D)$4,334.90 E)$4,368.81

Accepted Answer

Present value = $4,500/(1 + 0.025)³ = $4,178.70

Question 18

You have just made your first $5,000 contribution to your individual retirement account.Assuming you earn a 5 percent rate of return and make no additional contributions,what will your account be worth when you retire in 35 years? What if you wait for 5 years before contributing?
A)$26,335.37; $23,011.60
B)$27,311.20; $29,803.04
C)$27,311.20; $22,614.08
D)$27,580.08; 21,609.71
E)$31,241.90; $32,614.08

Accepted Answer

Future value _{35 years} = $5,000 × (1 + 0.05)³⁵ = $27,580.08Future value _{30 years} = $5,000 × (1 + 0.05)³⁰ = $21,609.71

Question 19

Assume the total cost of a college education will be $285,000 when your child enters college in 22 years.You presently have $35,000 to invest.What annual rate of interest must you earn on your investment to cover the cost of your child's college education?
A)8.65 percent
B)9.40 percent
C)10.00 percent
D)10.60 percent
E)11.00 percent

Accepted Answer

$285,000 = $35,000 × (1 + r)²²; r = 10.00 percent

Question 20

Suppose that in 2010,a $10 silver certificate from 1898 sold for $11,200.For this to have been true,what would the annual increase in the value of the certificate have been?
A)6.47 percent
B)6.81 percent
C)7.23 percent
D)7.49 percent
E)7.97 percent

Accepted Answer

$11,200 = $10 × (1 + r)^{(2010 - 1898)}; r = 6.47 percent

Quiz 4: Introduction to Valuation: The Time Value of Money

You want to have $25,000 for a down payment on a house 6 years from now.If you can earn 6.5 percent,compounded annually,on your savings,how much do you need to deposit today to reach your goal?

Your coin collection contains ten 1939 silver dollars.If your great grandparents purchased them for their face value when they were new,how much will your collection be worth when you retire in 2050,assuming they appreciate at a 5.1 percent annual rate?

Your friend claims that he invested $5,000 seven years ago and that this investment is worth $38,700 today.For this to be true,what annual rate of return did he have to earn? Assume the interest compounds annually.

Ten years from now,you will be inheriting $100,000.What is this inheritance worth to you today if you can earn 5.5 percent interest,compounded annually?

At 10 percent interest,how long does it take to quadruple your money?

You have been told that you need $25,600 today in order to have $100,000 when you retire 35 years from now.What rate of interest was used in the present value computation? Assume interest is compounded annually.

You want to have $45,000 in cash to buy a car 4 years from today.You expect to earn 4.5 percent,compounded annually,on your savings.How much do you need to deposit today if this is the only money you save for this purpose?

Today,Stacy is investing $26,000 at 6.0 percent,compounded annually,for 4 years.How much additional income could he earn if he had invested this amount at 7 percent,compounded annually?

Isaac only has $690 today but needs $800 to buy a new laptop.How long will he have to wait to buy the laptop if he earns 5.4 percent compounded annually on his savings?

You have $1,100 today and want to triple your money in 5 years.What interest rate must you earn if the interest is compounded annually?

You're trying to save to buy a new $210,000 Ferrari.You have $38,000 today that can be invested at your bank.The bank pays 4.1 percent annual interest on its accounts.How long will it be before you have enough to buy the car?

Planters Bank pays 5 percent simple interest on its savings account balances,whereas Centura Bank pays 5 percent compounded annually.If you made a $12,000 deposit in each bank,how much more money would you earn from your Centura Bank account at the end of 20 years?

You have $1,500 today in your savings account.How long must you wait for your savings to be worth $4,000 if you are earning 1.1 percent interest,compounded annually?

How long will it take to double your savings if you earn 7.2 percent interest,compounded annually?

You have just made your first $5,000 contribution to your individual retirement account.Assuming you earn a 5 percent rate of return and make no additional contributions,what will your account be worth when you retire in 35 years? What if you wait for 5 years before contributing?

Assume the total cost of a college education will be $285,000 when your child enters college in 22 years.You presently have $35,000 to invest.What annual rate of interest must you earn on your investment to cover the cost of your child's college education?

Suppose that in 2010,a $10 silver certificate from 1898 sold for $11,200.For this to have been true,what would the annual increase in the value of the certificate have been?