Question 1

Jessica invests $3,000 in an account that pays 5% simple interest. How much more could she have earned over a 7-year period if the interest had compounded annually?
A) $122.20
B) $129.20
C) $147.80
D) $171.30
E) $221.30

Accepted Answer

Using the simple interest formula, we can calculate that she would earn $1,050 in 7 years ($3,000 x 0.05 x 7 = $1,050).

Using the compound interest formula, we can calculate that she would earn $1,221.30 in 7 years if the interest was compounded annually.

The difference between these two amounts is $171.30, so the answer is D.

Question 2

Alexander Industries just had a very proﬁtable year. The owner has decided to invest $225,000 of the proﬁts in a venture that pays an 8% rate of return for ﬁfteen years. How much more would the
Investment have been worth if the owner could have made 9% on this investment?
A) $52,910.25
B) $105,820.50
C) $211,641.00
D) $713,738.05
E) $819,558.55

Accepted Answer

The answer of Alexander Industries just had a very proﬁtable...

Question 3

Andy promises Opie that he will give him $5,000 upon his graduation from college at Mayberry U. How much must Andy invest today to make good on his promise, if Opie is expected to graduate in
12 years and Andy can earn 5% on his money?
A) $2,135.32
B) $2,784.19
C) $2,881.11
D) $3,012.88
E) $8,979.28

Accepted Answer

To calculate how much Andy needs to invest today, we need to use the present value formula: PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the interest rate, and n is the number of periods. In this case, the future value is $5,000, the interest rate is 5%, and the number of periods is 12 (since Opie will graduate in 12 years). Plugging these values into the formula, we get:

PV = $5,000 / (1 + 0.05)^12
PV = $5,000 / 1.795856
PV = $2,784.19

Therefore, Andy needs to invest $2,784.19 today to make sure he can fulfill his promise to Opie upon his graduation from college.

Question 4

Stephen invests $2,500 in an account that pays 6% simple interest. How much money will Stephen have at the end of three years?
A) $2,650
B) $2,809
C) $2,950
D) $2,978
E) $3,000

Accepted Answer

Simple interest is calculated using the formula $I = P \times r \times t$, where $I$ is the interest, $P$ is the principal amount, $r$ is the rate of interest per period, and $t$ is the time. For Stephen's investment, $P = $2,500$, $r = 6\% = 0.06$, and $t = 3$ years. Thus, the interest earned is $I = $2,500 \times 0.06 \times 3 = $450$. Adding this interest to the principal gives the total amount as $P + I = $2,500 + $450 = $2,950$.

Question 5

You would like to invest some money today such that your investment will be worth $100,000 ﬁfteen years from now. Your broker gives you two options. First, you can invest at a guaranteed
Annual rate of 4%. Or, you can invest in stocks and hopefully earn an average of 7% per year. How
Much more will you have to invest today if you opt for the ﬁxed rate rather than the stocks?
A) $18,145.45
B) $18,419.02
C) $18,623.18
D) $18,904.21
E) $19,281.85

Accepted Answer

The answer of You would like to invest some money...

Question 6

You want to have $260,000 saved 15 years from now. How much less do you have to deposit today to reach this goal if you can earn 8% rather than 7% on your savings?
A) $8,728.44
B) $12,273.13
C) $16,602.12
D) $17,414.41
E) $20,019.2

Accepted Answer

We can use the formula for future value of a present sum:
FV = PV(1+r)^t
where FV is the future value, PV is the present value, r is the interest rate, and t is the time period.

If we let x be the amount we need to deposit today at 7%, then we can solve for x:
260,000 = x(1+0.07)^15
260,000 = x(2.546)
x = 102,184.93

Now, we can use the same formula to find out how much we need to deposit today at 8% to reach the same future value of $260,000:
260,000 = PV(1+0.08)^15
PV = 102,184.93(1.08/1.07)^15
PV = 89,911.80

The difference between the two amounts is:
102,184.93 - 89,911.80 = 12,273.13

Therefore, we need to deposit $12,273.13 less today at 8% in order to reach the same goal of $260,000 in 15 years.

Question 7

How much would you have to invest today at 8% compounded annually to have $25,000 available for the purchase of a car four years from now?
A) $18,267.26
B) $18,375.75
C) $19,147.25
D) $21,370.10
E) $22,149.57

Accepted Answer

The answer of How much would you have to invest...

Question 8

What is the present value of $2,800 to be received three years from now if the discount rate is 9.5%?
A) $2,114.48
B) $2,132.63
C) $2,361.48
D) $2,734.54
E) $3,676.21

Accepted Answer

The answer of What is the present value of $2,800...

Question 9

Alex and Courtney are each investing $1,200 today in a savings account. Alex will earn 4% interest compounded annually. Courtney will earn 4% simple interest. After ﬁve years Alex will have ____
More than Courtney.
A) $19.98
B) $20.13
C) $20.17
D) $20.21
E) $20.28

Accepted Answer

Alex's investment with compound interest will grow slightly more than Courtney's with simple interest. The difference after five years is $19.98.

Question 10

Twenty years from now, you would like to purchase a cottage located on the shores of your favourite lake. You expect that you will have $250,000 available at that time for this purchase. You
Could afford a home that is currently selling for ____ if the homes increase in value by 3% annually,
But if the homes increase in value by 5% annually, you can only afford a home priced at _____
Today.
A) $127,023; $92,687
B) $138,419; $94,222
C) $138,419; $114,097
D) $144,676; $100,469
E) $144,676; $111,068

Accepted Answer

The answer of Twenty years from now, you would like...

Question 11

You would like to give your daughter $40,000 towards her college education thirteen years from now. How much money must you set aside today for this purpose if you can earn 6.3% on your
Funds?
A) $17,750.00
B) $17,989.28
C) $18,077.05
D) $18,213.69
E) $18,395.00

Accepted Answer

To find the present value, use the formula for present value of a future sum: PV = FV / (1 + r)^n, where FV is the future value ($40,000), r is the interest rate (6.3% or 0.063), and n is the number of years (13). Calculating this gives approximately $18,077.05.

Question 12

When you retire forty years from now, you want to have $1 million. You think you can earn an average of 8.5% on your money. To meet this goal, you are trying to decide whether to deposit a
Lump sum today, or to wait and deposit a lump sum ﬁve years from today. How much more will you
Have to deposit as a lump sum if you wait for ﬁve years before making the deposit?
A) $18,001.06
B) $18,677.78
C) $18,998.03
D) $19,272.81
E) $21,036.83

Accepted Answer

The answer of When you retire forty years from now,...

Question 13

You own a stamp collection that is currently valued at $24,500. If the value increases by 5.5% annually, how much will the collection be worth when you retire 40 years from now?
A) $204,113.07
B) $204,981.16
C) $205,155.45
D) $206,666.67
E) $208,576.07

Accepted Answer

The answer of You own a stamp collection that is...

Question 14

When you retire 36 years from now, you want to have $2 million. You think you can earn an average of 11.5% on your investments. To meet your goal, you are trying to decide whether to deposit a lump
Sum today, or to wait and deposit a lump sum 3 years from today. How much more will you have to
Deposit as a lump sum if you wait for 3 years before making the deposit?
A) $15,344.14
B) $15,677.78
C) $16,208.11
D) $17,021.12
E) $19,407.78

Accepted Answer

The correct answer is A.The present value of $2 million in 36 years at 11.5% is $273,224.14. If you wait 3 years to deposit the lump sum, you will have to deposit $15,344.14 more to reach the same goal.

Question 15

Your grandmother invested one lump sum 17 years ago at 4.25% interest. Today, she gave you the proceeds of that investment which totaled $5,539.92. How much did your grandmother originally
Invest?
A) $2,700.00
B) $2,730.30
C) $2,750.00
D) $2,768.40
E) $2,774.90

Accepted Answer

The answer of Your grandmother invested one lump sum 17...

Question 16

What is the future value of $3,497 invested for 15 years at 7.5% compounded annually?
A) $7,431.13
B) $10,347.19
C) $14,289.16
D) $14,911.08
E) $15,267.21

Accepted Answer

The answer of What is the future value of $3,497...

Question 17

Today Richard is investing $1,000 at 5% interest for ﬁve years. One year ago, Richard invested $1,000 at 6.25% for six years. How much money will Richard have saved in total ﬁve years from now
If both investments compound interest annually?
A) $2,543.77
B) $2,641.98
C) $2,678.81
D) $2,630.36
E) $2,714.99

Accepted Answer

The answer of Today Richard is investing $1,000 at 5%...

Question 18

You would like to give your daughter $50,000 towards her college education sixteen years from now. How much money must you set aside today for this purpose if you can earn 7.8% on your
Funds?
A) $14,775.50
B) $15,033.84
C) $15,250.00
D) $16,245.33
E) $16,909.13

Accepted Answer

To calculate the present value, we use the formula: PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years. 
Substituting the values given, we get: 
PV = 50,000 / (1 + 0.078)^16
PV = 50,000 / 3.866 
PV = $15,033.84 
Therefore, you should set aside $15,033.84 today to have $50,000 for your daughter’s college education sixteen years from now.

Question 19

What is the present value of $36,800 to be received 6 years from today if the discount rate is 12%?
A) $18,644.03
B) $19,407.18
C) $19,414.14
D) $20,211.08
E) $20,390.14

Accepted Answer

The answer of What is the present value of $36,800...

Question 20

Last year, you deposited $25,000 into a retirement savings account at a ﬁxed rate of 7.5%. Today, you could earn a ﬁxed rate of 8% on a similar type account. However, your rate is ﬁxed and cannot
Be adjusted. How much less could you have deposited last year if you could have earned a ﬁxed
Rate of 8% and still have the same amount as you currently will when you retire 40 years from
Today?
A) $1,218.46 less
B) $1,666.67 less
C) $2,408.28 less
D) $3,628.09 less
E) $4,331.30 less

Accepted Answer

The answer of Last year, you deposited $25,000 into a...

Quiz 5: Introduction to Valuation: the Time Value of Money

Jessica invests $3,000 in an account that pays 5% simple interest. How much more could she have earned over a 7-year period if the interest had compounded annually?

Alexander Industries just had a very proﬁtable year. The owner has decided to invest $225,000 of the proﬁts in a venture that pays an 8% rate of return for ﬁfteen years. How much more would the Investment have been worth if the owner could have made 9% on this investment?

Andy promises Opie that he will give him $5,000 upon his graduation from college at Mayberry U. How much must Andy invest today to make good on his promise, if Opie is expected to graduate in 12 years and Andy can earn 5% on his money?

Stephen invests $2,500 in an account that pays 6% simple interest. How much money will Stephen have at the end of three years?

You want to have $260,000 saved 15 years from now. How much less do you have to deposit today to reach this goal if you can earn 8% rather than 7% on your savings?

How much would you have to invest today at 8% compounded annually to have $25,000 available for the purchase of a car four years from now?

What is the present value of $2,800 to be received three years from now if the discount rate is 9.5%?

Alex and Courtney are each investing $1,200 today in a savings account. Alex will earn 4% interest compounded annually. Courtney will earn 4% simple interest. After ﬁve years Alex will have ____ More than Courtney.

You would like to give your daughter $40,000 towards her college education thirteen years from now. How much money must you set aside today for this purpose if you can earn 6.3% on your Funds?

You own a stamp collection that is currently valued at $24,500. If the value increases by 5.5% annually, how much will the collection be worth when you retire 40 years from now?

Your grandmother invested one lump sum 17 years ago at 4.25% interest. Today, she gave you the proceeds of that investment which totaled $5,539.92. How much did your grandmother originally Invest?

What is the future value of $3,497 invested for 15 years at 7.5% compounded annually?

Today Richard is investing $1,000 at 5% interest for ﬁve years. One year ago, Richard invested $1,000 at 6.25% for six years. How much money will Richard have saved in total ﬁve years from now If both investments compound interest annually?

You would like to give your daughter $50,000 towards her college education sixteen years from now. How much money must you set aside today for this purpose if you can earn 7.8% on your Funds?

What is the present value of $36,800 to be received 6 years from today if the discount rate is 12%?