Question 1

At an annual interest rate of 10 percent,about how many years will it take $100 to double in value?
A) 5
B) 7
C) 9
D) 11

Accepted Answer

To double the initial value, the final amount must be twice as much as the initial amount. Therefore, we need to solve for the number of years it takes for $100 to grow to $200 with an annual interest rate of 10%.

We can use the formula for compound interest:

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

where:

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

In this case, we have:

P = $100
A = $200
r = 0.10
n = 1 (interest is compounded annually)

Plugging these values into the formula, we get:

$200 = $100(1 + 0.10/1)^(1t)

Simplifying:

2 = 1.1^t

Taking the natural logarithm of both sides:

ln(2) = ln(1.1^t)

Using the property of logarithms that allows us to bring the exponent down:

ln(2) = t*ln(1.1)

Solving for t:

t = ln(2) / ln(1.1)

Using a calculator, we get:

t ≈ 6.73

Rounding to the nearest whole number, we get:

t ≈ 7

Therefore, it will take about 7 years for $100 to double in value at an annual interest rate of 10%. The best choice is B.

Question 2

Which of the following is the correct way to compute the future value of $X that earns r percent interest for N years? A) $X(1 + rN)^N B) $X(1 + r)^N C) $X(1 + rN) D) $X(1 + r/N)N

Accepted Answer

The correct formula for calculating the future value of X with interest rate r for N years is:

X(1 + r)^N

Option B is the only choice that matches this formula, with (1 + r) raised to the power of N. Option A has rN without parentheses, which would lead to incorrect results, and options C and D are not the correct formulas for future value with compound interest. Therefore, the best choice is B.

Question 3

What is the future value of $750 one year from today if the interest rate is 3 percent?
A) 772.73
B) 772.50
C) 773.33
D) None of the above are correct to the nearest cent.

Accepted Answer

The future value (FV) can be calculated using the formula: 
FV = PV * (1 + r)^n 
where PV is the present value, r is the interest rate, and n is the number of periods (in this case, one year). 
Substituting the values given: 
FV = 750 * (1 + 0.03)^1 = 772.50 
Therefore, the correct answer is B.

Question 4

The future value of a deposit in a savings account will be smaller
A) the longer a person waits to withdraw the funds.
B) the lower the interest rate is.
C) the larger the initial deposit is.
D) All of the above are correct.

Accepted Answer

The future value of a deposit in a savings account is directly proportional to the interest rate. So, the lower the interest rate, the smaller the future value will be. The time and initial deposit amount may affect the amount earned, but they do not necessarily make the future value smaller.

Question 5

A manufacturing company is thinking about building a new factory.The factory,if built,will yield the company $300 million in 7 years,and it would cost $220 million today to build.The company will decide to build the factory if the interest rate is
A) no less than 4.53 percent.
B) no greater than 4.53 percent.
C) no less than 5.81 percent.
D) no greater than 5.81 percent.

Accepted Answer

To determine whether the company should build the factory, we need to compare the present value of the future revenue ($300 million) to the cost of building the factory ($220 million). We can 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 years.

Substituting in the values given:

220 = 300 / (1 + r)^7

Solving for r:

(1 + r)^7 = 300 / 220
1 + r = (300 / 220)^(1/7)
r = (300 / 220)^(1/7) - 1
r ≈ 0.0453, or 4.53%

Therefore, the company will decide to build the factory if the interest rate is no greater than 4.53%. This means that if the interest rate is lower than 4.53%, the present value of the future revenue would be greater than the cost of building the factory, making it a profitable investment for the company.

Question 6

If you put $250 into an account with a 4 percent interest rate,how many years would you have to wait to have $370.06?
A) 10
B) 14
C) 17
D) 20

Accepted Answer

The answer of If you put $250 into an account...

Question 7

At an annual interest rate of 14 percent,about how many years will it take $100 to double in value?
A) 3
B) 4
C) 5
D) 7

Accepted Answer

Using the rule of 72 (72 divided by the interest rate), it would take approximately 5 years for $100 to double at an annual interest rate of 14 percent. Therefore, the best choice is C - 5 years.

Question 8

Which of the following is the correct way to compute the future value of $1 put into an account that earns 5 percent interest for 20 years? A) $1(1 + .05)²⁰ B) $1(1 + .0520)20 C) $1(1 + .0520) D) $1(1 + 20/.05)²⁰

Accepted Answer

The future value of an investment is calculated using the formula FV = PV(1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of periods. Here, PV = $1, r = 0.05, and n = 20.

Question 9

Which of the following is the correct way to compute the future value of $100 put into an account that earns 4 percent interest for 10 years? A) $100(1 + .04¹⁰) B) $100(1 + .0410) C) $100 x 10 x (1 + .04) D) $100(1 + .04)¹⁰

Accepted Answer

The future value of an investment is calculated using the formula FV = PV(1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of periods. Here, PV = $100, r = 0.04, and n = 10.

Question 10

Suppose you are deciding whether or not to buy a particular bond.If you buy the bond and hold it for 5 years,then at that time you will receive a payment of $10,000.If the interest rate is 6 percent,you will buy the bond if its price today is no greater than
A) $8,225.06.
B) $7,652.58.
C) $7,472.58.
D) $6,998.98.

Accepted Answer

To determine whether or not it is worth buying the bond, we need to calculate its present value using 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.

In this case, we know that FV = $10,000, r = 6%, and n = 5. Plugging these values into the formula, we get:

PV = $10,000 / (1 + 0.06)^5 
PV = $7,472.58

Therefore, you should only buy the bond if its price today is no greater than $7,472.58.

Question 11

If you presently have $50,000 saved and earn 15 percent interest per year,about how many years will it take for your investment to triple?
A) 6
B) 8
C) 10
D) 12

Accepted Answer

The answer of If you presently have $50,000 saved and...

Question 12

At an annual interest rate of 10 percent,about how many years will it take $100 to triple in value?
A) 8
B) 10
C) 12
D) 14

Accepted Answer

To triple $100, the final amount will be $300. 
Using the formula for compound interest, we can solve for the number of years: 
$300 = $100(1 + 0.10)^n 
3 = (1.10)^n 
log(3) = n*log(1.10) 
n = log(3)/log(1.10) 
n ≈ 12 years. 
Therefore, the best choice is C.

Question 13

What is the future value of $450 at an interest rate of 15 percent two years from today?
A) $525.87
B) $566.00
C) $585.00
D) $595.13

Accepted Answer

Using the formula for future value of a single sum:
FV = PV x (1 + r)^n
where FV = future value
PV = present value
r = interest rate
n = number of years

Plugging in the given values:
FV = $450 x (1 + 0.15)^2
FV = $595.13

Therefore, the correct answer is D.

Question 14

What is the future value of $333 at an interest rate of 3 percent one year from today?
A) $337.39
B) $342.99
C) $343.09
D) None of the above are correct to the nearest cent.

Accepted Answer

The answer of What is the future value of $333...

Question 15

The future value of a deposit in a savings account will be larger
A) the longer a person waits to withdraw the funds.
B) the higher the interest rate is.
C) the larger the initial deposit is.
D) All of the above are correct.

Accepted Answer

The future value of a deposit in a savings account will be larger if a person waits longer to withdraw the funds because more interest will have accrued on the principal amount. The future value will also be larger if the interest rate is higher because more interest will be earned on the principal amount. Additionally, a larger initial deposit will result in a larger future value because there is more money in the account to earn interest. Therefore, all of the options are correct.

Question 16

Suppose you are deciding whether or not to buy a particular bond for $2,990.08.If you buy the bond and hold it for 5 years,then at that time you will receive a payment of $5,000.You will buy the bond today if the interest rate is
A) no less than 9.48 percent.
B) no greater than 9.48 percent.
C) no less than 10.83 percent.
D) no greater than 10.83 percent.

Accepted Answer

The answer of Suppose you are deciding whether or not...

Question 17

What is the future value of $800 one year from today if the interest rate is 7 percent?
A) $747.66
B) $756.00
C) $856.00
D) None of the above are correct to the nearest cent.

Accepted Answer

The answer of What is the future value of $800...

Question 18

You put $75 in the bank one year ago and forgot about it.The bank sends you a notice that you now have $81 in your account.What interest rate did you earn?
A) 5 percent
B) 6 percent
C) 7 percent
D) 8 percent

Accepted Answer

The answer of You put $75 in the bank one...

Question 19

What is the future value of $500 one year from today if the interest rate is 4 percent?
A) $515
B) $520
C) $530
D) None of the above is correct.

Accepted Answer

To calculate the future value, we use the formula: FV = PV x (1 + r), where FV is the future value, PV is the present value, and r is the interest rate as a decimal. Plugging in the values, we get: FV = $500 x (1 + 0.04) = $520. Therefore, the answer is B) $520.

Question 20

At an annual interest rate of 20 percent,about how many years will it take $100 to triple in value?
A) 5
B) 6
C) 8
D) 9

Accepted Answer

Using the formula for compound interest, we can find the time it takes for the initial investment to triple: 
$100(1+0.20)^t = $300 
Simplifying, 
$(1.20)^t = 3$ 
Taking the logarithm of both sides, 
$t \log(1.20) = \log(3)$ 
Solving for t, 
$t = \frac{\log(3)}{\log(1.20)} \approx 5.9$ 
Rounding up to the nearest integer, it would take 6 years for $100 to triple at a 20% annual interest rate. Therefore, the best choice is B.

Quiz 27: The Basic Tools of Finance

At an annual interest rate of 10 percent,about how many years will it take $100 to double in value?

Which of the following is the correct way to compute the future value of $X that earns r percent interest for N years?

What is the future value of $750 one year from today if the interest rate is 3 percent?

The future value of a deposit in a savings account will be smaller

A manufacturing company is thinking about building a new factory.The factory,if built,will yield the company $300 million in 7 years,and it would cost $220 million today to build.The company will decide to build the factory if the interest rate is

If you put $250 into an account with a 4 percent interest rate,how many years would you have to wait to have $370.06?

At an annual interest rate of 14 percent,about how many years will it take $100 to double in value?

Which of the following is the correct way to compute the future value of $1 put into an account that earns 5 percent interest for 20 years?

Which of the following is the correct way to compute the future value of $100 put into an account that earns 4 percent interest for 10 years?

Suppose you are deciding whether or not to buy a particular bond.If you buy the bond and hold it for 5 years,then at that time you will receive a payment of $10,000.If the interest rate is 6 percent,you will buy the bond if its price today is no greater than

If you presently have $50,000 saved and earn 15 percent interest per year,about how many years will it take for your investment to triple?

At an annual interest rate of 10 percent,about how many years will it take $100 to triple in value?

What is the future value of $450 at an interest rate of 15 percent two years from today?

What is the future value of $333 at an interest rate of 3 percent one year from today?

The future value of a deposit in a savings account will be larger

Suppose you are deciding whether or not to buy a particular bond for $2,990.08.If you buy the bond and hold it for 5 years,then at that time you will receive a payment of $5,000.You will buy the bond today if the interest rate is

What is the future value of $800 one year from today if the interest rate is 7 percent?

You put $75 in the bank one year ago and forgot about it.The bank sends you a notice that you now have $81 in your account.What interest rate did you earn?

What is the future value of $500 one year from today if the interest rate is 4 percent?

At an annual interest rate of 20 percent,about how many years will it take $100 to triple in value?