Question 1

Marti's coin collection contains fifty 1948 silver dollars. Her grandparents purchased them at their face value in 1948. These coins have appreciated by 7.6 percent annually. How much will the collection be worth in 2025?
A) $13,611.18
B) $18,987.56
C) $14,122.01
D) $11,218.27
E) $14,077.16

Accepted Answer

The answer of Marti's coin collection contains fifty 1948 silver...

Question 2

Suppose the first comic book of a classic series was sold in 1954. In 2017, the estimated price for this comic book was $310,000, which is an annual return of 22 percent. For this to be true, what was the original price of the comic book in 1954?
A) $1.00
B) $.97
C) $1.33
D) $1.12
E) $1.20

Accepted Answer

The original price of the comic book can be calculated using the formula:Original price = Estimated price / (1 + annual return)^number of yearsIn this case, the estimated price is $310,000, the annual return is 22%, and the number of years is 2017 - 1954 = 63.Plugging these values into the formula, we get:Original price = $310,000 / (1 + 0.22)^63 = $1.12

Question 3

You just invested $49,000 that you received as an insurance settlement. How much more will this account be worth in 40 years if you earn an average return of 7.6 percent rather than just 7.1 percent?
A) $59,818.92
B) $98,509.16
C) $140,423.33
D) $155,986.70
E) $138,342.91

Accepted Answer

We can use the compound interest formula to calculate the future value of the investment with a 7.1% return:

FV = PV(1 + r)^n
FV = 49,000(1 + 0.071)^40
FV = 333,829.18

Now we can use the same formula with a 7.6% return:

FV = PV(1 + r)^n
FV = 49,000(1 + 0.076)^40
FV = 489,815.88

The difference between these two future values is:

FV at 7.6% - FV at 7.1% = 489,815.88 - 333,829.18 = 155,986.70

Therefore, the account will be worth $155,986.70 more in 40 years if the average return is increased from 7.1% to 7.6%. The answer is D.

Question 4

You will receive $15,000 in two years when you graduate. You plan to invest this at an annual interest rate of 6.5 percent. How much money will you have 8 years from now?
A) $24,824.94
B) $19,381.16
C) $21,887.13
D) $23,209.19
E) $20,414.73

Accepted Answer

To find the future value, use the formula FV = PV * (1 + r)^n. Here, PV = $15,000, r = 6.5% or 0.065, and n = 6 years (since the money is invested for 6 years after receiving it in 2 years). FV = 15000 * (1 + 0.065)^6 = $21,887.13.

Question 5

Today, you earn a salary of $31,000. What will be your annual salary ten years from now if you receive annual raises of 2.2 percent?
A) $38,536.36
B) $37,414.06
C) $38,235.24
D) $37,122.08
E) $36,736.00

Accepted Answer

To calculate the future salary, use the formula for compound interest: Future Salary = Present Salary * (1 + raise rate)^number of years. Here, $31,000 * (1 + 0.022)^10 = $38,536.36.

Question 6

You hope to buy your dream car five years from now. Today, that car costs $62,500. You expect the price to increase by an average of 2.9 percent per year. How much will your dream car cost by the time you are ready to buy it?
A) $73,340.00
B) $68,666.67
C) $72,103.59
D) $66,818.02
E) $69,023.16

Accepted Answer

To solve this problem, we need to use the formula for compound interest:

FV = PV * (1 + r)^n

where FV is the future value, PV is the present value, r is the annual interest rate as a decimal, and n is the number of years.

In this case, PV = $62,500, r = 0.029, and n = 5. Plugging these values into the formula, we get:

FV = $62,500 * (1 + 0.029)^5
FV = $72,103.59

Therefore, the answer is Choice C: $72,103.59.

Question 7

You own a classic car currently valued at $64,000. If the value increases by 2.5 percent annually, how much will the car be worth 15 years from now?
A) $94,035.00
B) $86,008.17
C) $80,013.38
D) $92,691.08
E) $91,480.18

Accepted Answer

The answer of You own a classic car currently valued...

Question 8

You invested $6,500 at 6 percent simple interest. How much more could you have earned over a 10-year period if the interest had compounded annually?
A) $1,049.22
B) $930.11
C) $1,182.19
D) $1,201.15
E) $1,240.51

Accepted Answer

To calculate the difference between simple interest and compound interest over a 10-year period, we first calculate both types of interest on the $6,500 investment at 6 percent.Simple Interest = Principal × Rate × Time = $6,500 × 0.06 × 10 = $3,900Compound Interest = Principal × (1 + Rate)^Time - Principal = $6,500 × (1 + 0.06)^10 - $6,500 = $6,500 × (1.790847) - $6,500 = $11,640.51 - $6,500 = $5,140.51Difference = Compound Interest - Simple Interest = $5,140.51 - $3,900 = $1,240.51

Question 9

You have a savings account valued at $1,500 today that earns an annual interest rate of 8.7 percent. How much more would this account be worth if you wait to spend the entire balance in 25 years rather than in 20 years?
A) $6,306.16
B) $4,658.77
C) $3,311.18
D) $6,907.17
E) $4,117.64

Accepted Answer

The answer of You have a savings account valued at...

Question 10

This morning, DJ's invested $225,000 to help fund future projects. How much additional money will the firm have three years from now if it can earn an annual interest rate of 4 percent rather than 3.5 percent?
A) $3,391.90
B) $3,632.88
C) $3,008.17
D) $4,219.68
E) $3,711.08

Accepted Answer

To find the additional money the firm will have, we calculate the future value of the investment at both interest rates and subtract the lower from the higher. At 4% interest, the future value (FV) is calculated using the formula FV = P(1 + r)^n, where P is the principal amount ($225,000), r is the annual interest rate (0.04), and n is the number of years (3). This gives us FV = $225,000 * (1 + 0.04)^3 = $225,000 * 1.124864 = $253,094.40.At 3.5% interest, the future value is FV = $225,000 * (1 + 0.035)^3 = $225,000 * 1.108817 = $249,461.52.The difference between the two future values is $253,094.40 - $249,461.52 = $3,632.88.

Question 11

Today, you have two coins each of which is valued at $100. One coin is expected to appreciate by 5.2 percent annually while the other coin should appreciate by 5.7 percent annually. What will be the difference in the value of the two coins 50 years from now?
A) $337.43
B) $318.04
C) $191.79
D) $128.32
E) $380.15

Accepted Answer

To find the difference in value after 50 years, calculate the future value of each coin using the formula FV = PV * (1 + r)^n. For the first coin: FV1 = $100 * (1 + 0.052)^50. For the second coin: FV2 = $100 * (1 + 0.057)^50. The difference is FV2 - FV1 = $1,898.29 - $1,560.86 = $337.43.

Question 12

What is the future value of $11,600 invested for 17 years at 7.25 percent compounded annually?
A) $32,483.60
B) $27,890.87
C) $38,991.07
D) $41,009.13
E) $38,125.20

Accepted Answer

The answer of What is the future value of $11,600...

Question 13

Your father invested a lump sum 28 years ago at 4.05 percent annual interest. Today, he gave you the proceeds of that investment, totalling $48,613.24. How much did your father originally invest?
A) $14,929.47
B) $16,500.00
C) $15,994.70
D) $15,500.00
E) $16,099.45

Accepted Answer

The original investment can be calculated using the formula for compound interest: $A = P(1 + r)^n$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), and $n$ is the time the money is invested for in years. Rearranging the formula to solve for $P$ gives $P = A / (1 + r)^n$. Substituting the given values ($A = 48613.24$, $r = 0.0405$, $n = 28$) into the formula gives $P = 48613.24 / (1 + 0.0405)^{28}$, which calculates to approximately $15,994.70.

Question 14

Twenty years from now, you want to spend $175,000 for a fancy car. How much must you deposit as a lump sum today to achieve this goal at an annual interest rate of 6.6 percent?
A) $54,208.16
B) $48,740.95
C) $57,911.08
D) $40,019.82
E) $51,446.60

Accepted Answer

We can use the formula for present value of a lump sum:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the annual interest rate, and n is the number of periods.

In this case, FV = $175,000, r = 6.6%, and n = 20 (since we want the money 20 years from now). Substituting these values, we get:

PV = $175,000 / (1 + 0.066)^20
PV = $48,740.95

Therefore, the amount that must be deposited as a lump sum today to achieve the goal is $48,740.95. Choice (B) is the correct answer.

Question 15

Alex invested $2,550 in an account that pays 5 percent simple interest. How much money will he have at the end of four years?
A) $2,650.00
B) $3,100.26
C) $3,060.00
D) $3,250.00
E) $3,099.54

Accepted Answer

Simple interest formula:

I = P * r * t

Where: 
I = Interest earned 
P = Principal amount 
r = Interest rate 
t = Time in years

Given: 
P = $2,550 
r = 0.05 
t = 4 years

Plugging in the values, we get:

I = $2,550 * 0.05 * 4 = $510

Total amount at the end of 4 years:

Amount = Principal + Interest

Amount = $2,550 + $510 = $3,060

Therefore, the best choice is C.

Question 16

You just received a $5,000 gift from your grandmother which you have decided to save and then gift to your grandchildren 50 years from now. How much additional money will you gift if you earn 7.5 percent interest rather than 7 percent interest over the next 50 years?
A) $39,318.09
B) $39,464.79
C) $38,211.16
D) $37,811.99
E) $38,663.60

Accepted Answer

The answer of You just received a $5,000 gift from...

Question 17

Travis invested $8,000 in an account that pays 4 percent simple interest. How much more could he have earned over a 7-year period if the interest had compounded annually?
A) $291.41
B) $287.45 
C) $302.16
D) $266.67
E) $258.09

Accepted Answer

The answer of Travis invested $8,000 in an account that...

Question 18

You are depositing $4,500 today at an annual interest rate of 7.2 percent. How much additional interest will you earn if you leave the money invested for 45 years instead of 40 years?
A) $25,723.08
B) $30,185.14
C) $22,441.56
D) $6,370.69
E) $11,590.93

Accepted Answer

Using the formula for compound interest, we have:

A = P(1 + r/n)^(nt)

where:

A = final amount
P = initial deposit
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = number of years

If we assume the interest is compounded annually (n = 1), we can find the final amount after 40 years:

A1 = 4500(1 + 0.072/1)^(1*40) = $51,880.88

Similarly, we can find the final amount after 45 years:

A2 = 4500(1 + 0.072/1)^(1*45) = $82,066.02

The difference in interest earned is:

A2 - A1 = $82,066.02 - $51,880.88 = $30,185.14

Therefore, the additional interest earned by leaving the money invested for 45 years instead of 40 years is $30,185.14.

The correct answer is B.

Question 19

Al invested $3,630 in an account that pays 6 percent simple interest. How much money will he have at the end of five years?
A) $4,910
B) $5,056
C) $4,719
D) $4,678
E) $5,299

Accepted Answer

To calculate the total amount of money Al will have at the end of five years with simple interest, use the formula: Total Amount = Principal + (Principal * Rate * Time). Here, Principal = $3,630, Rate = 6% or 0.06, and Time = 5 years. So, Total Amount = $3,630 + ($3,630 * 0.06 * 5) = $3,630 + $1,089 = $4,719.

Question 20

Phillippe invested $1,000 ten years ago and expected to have $1,800 today He has neither added nor withdrawn any money since his initial investment. All interest was reinvested and compounded annually. As it turns out, he only has $1,680 in his account today. Which one of the following must be true?
A) He earned simple interest rather than compound interest.
B) He earned a lower interest rate than he expected.
C) He did not earn any interest on interest as he expected.
D) He ignored the Rule of 72 which caused his account to decrease in value.
E) The future value interest factor turned out to be higher than he expected.

Accepted Answer

If Phillippe earned compound interest at the expected rate, he should have $1,800 in his account today. The fact that he only has $1,680 means that he earned a lower interest rate than he expected. Simple interest, answer A, would result in an even lower value than $1,680. Answer C is incorrect because the reinvestment of interest is the definition of compound interest. Answer D is irrelevant since the Rule of 72 is a method for estimating the time it takes an investment to double, not for calculating the actual value of an investment. Answer E is also irrelevant because the future value interest factor is just a tool to calculate the future value of an investment based on its interest rate, time, and compounding frequency, but it does not affect the actual performance of the investment.

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

Marti's coin collection contains fifty 1948 silver dollars. Her grandparents purchased them at their face value in 1948. These coins have appreciated by 7.6 percent annually. How much will the collection be worth in 2025?

Suppose the first comic book of a classic series was sold in 1954. In 2017, the estimated price for this comic book was $310,000, which is an annual return of 22 percent. For this to be true, what was the original price of the comic book in 1954?

You just invested $49,000 that you received as an insurance settlement. How much more will this account be worth in 40 years if you earn an average return of 7.6 percent rather than just 7.1 percent?

You will receive $15,000 in two years when you graduate. You plan to invest this at an annual interest rate of 6.5 percent. How much money will you have 8 years from now?

Today, you earn a salary of $31,000. What will be your annual salary ten years from now if you receive annual raises of 2.2 percent?

You hope to buy your dream car five years from now. Today, that car costs $62,500. You expect the price to increase by an average of 2.9 percent per year. How much will your dream car cost by the time you are ready to buy it?

You own a classic car currently valued at $64,000. If the value increases by 2.5 percent annually, how much will the car be worth 15 years from now?

You invested $6,500 at 6 percent simple interest. How much more could you have earned over a 10-year period if the interest had compounded annually?

You have a savings account valued at $1,500 today that earns an annual interest rate of 8.7 percent. How much more would this account be worth if you wait to spend the entire balance in 25 years rather than in 20 years?

This morning, DJ's invested $225,000 to help fund future projects. How much additional money will the firm have three years from now if it can earn an annual interest rate of 4 percent rather than 3.5 percent?

Today, you have two coins each of which is valued at $100. One coin is expected to appreciate by 5.2 percent annually while the other coin should appreciate by 5.7 percent annually. What will be the difference in the value of the two coins 50 years from now?

What is the future value of $11,600 invested for 17 years at 7.25 percent compounded annually?

Your father invested a lump sum 28 years ago at 4.05 percent annual interest. Today, he gave you the proceeds of that investment, totalling $48,613.24. How much did your father originally invest?

Twenty years from now, you want to spend $175,000 for a fancy car. How much must you deposit as a lump sum today to achieve this goal at an annual interest rate of 6.6 percent?

Alex invested $2,550 in an account that pays 5 percent simple interest. How much money will he have at the end of four years?

You just received a $5,000 gift from your grandmother which you have decided to save and then gift to your grandchildren 50 years from now. How much additional money will you gift if you earn 7.5 percent interest rather than 7 percent interest over the next 50 years?

Travis invested $8,000 in an account that pays 4 percent simple interest. How much more could he have earned over a 7-year period if the interest had compounded annually?

You are depositing $4,500 today at an annual interest rate of 7.2 percent. How much additional interest will you earn if you leave the money invested for 45 years instead of 40 years?

Al invested $3,630 in an account that pays 6 percent simple interest. How much money will he have at the end of five years?