Question 1

At which interest rate is the present value of $168.54 two years from today equal to $150 today?
A) 4 percent
B) 5 percent
C) 6 percent
D) None of the above would give a present value within a cent of $162.24.

Accepted Answer

We can use the formula for present value of a future amount:

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.

Substituting the given values, we get:

150 = 168.54/(1 + r)^2

Solving for r, we get:

r = 6%

Therefore, the answer is (C) 6 percent.

Question 2

You are expecting to receive $3,500 at some time in the future. Which of the following would unambiguously increase the present value of this future payment?
A) Interest rates rise and you get the payment sooner.
B) Interest rates rise and you have to wait longer for the payment.
C) Interest rates fall and you get the payment sooner.
D) Interest rates fall and you have to wait longer to get the payment.

Accepted Answer

The answer of You are expecting to receive $3,500 at...

Question 3

Which of the following is the correct expression for finding the present value of a $1,000 payment one year from today if the interest rate is 6 percent? A) $1,000 (1.06) B) $1,000^(1.06) C) $1,000/(1.06) D) None of the above is correct.

Accepted Answer

The correct expression for finding the present value of a future payment is to divide the payment amount by (1 + interest rate). Therefore, the correct expression for finding the present value of a $1,000 payment one year from today if the interest rate is 6 percent is $1,000/(1.06). Option A is the formula for finding the future value of a present payment, while option B is not a valid financial expression.

Question 4

You want to have $100,000 in five years. If the interest rate is 8 percent, about how much do you need to have today?
A) $66,225.25
B) $67,556.42
C) $68,058.32
D) $71,428.57

Accepted Answer

The answer of You want to have $100,000 in five...

Question 5

At which interest rate is the present value of $80.25 one year from today equal to $75 today?
A) 4 percent
B) 5 percent
C) 6 percent
D) 7 percent

Accepted Answer

The answer of At which interest rate is the present...

Question 6

What is the present value of a payment of $100 one year from today if the interest rate is 5 percent?
A) $95.50
B) $95.24
C) $95.00
D) None of the above are correct to the nearest cent.

Accepted Answer

The present value can be calculated 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 time periods. Plugging in the given values, we get PV = 100/(1+0.05)^1 = $95.24. Therefore, the best choice is B.

Question 7

Which of the following is the correct expression for finding the present value of a $500 payment two years from today if the interest rate is 6 percent? A) $500/(1.06)² B) $500 - 500(1.06)² C) $500/(1.02)⁶ D) None of the above is correct.

Accepted Answer

The present value formula is 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.

Substituting the values given in the question, we get: 
PV = 500 / (1 + 0.06)^2 
PV = 500 / 1.1236 
PV = $445.44

Therefore, the correct expression is: $500/(1.06)^2 = $445.44, which is choice A.

Question 8

You have been promised a payment of $400 in the future. In which of the following cases is the present value of this payment the lowest?
A) You receive the payment 4 years from now and the interest rate is 4 percent.
B) You receive the payment 4 years from now and the interest rate is 5 percent.
C) You receive the payment 5 years from now and the interest rate is 4 percent.
D) You receive the payment 5 years from now and the interest rate is 5 percent.

Accepted Answer

The answer of You have been promised a payment of...

Question 9

At which interest rate is the present value of $95.40 one year from today equal to $90 today?
A) 4 percent
B) 5 percent
C) 6 percent
D) 7 percent

Accepted Answer

We can use the present value formula to solve for the interest rate:

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.

Plugging in the given values, we get:

90 = 95.40 / (1 + r)^1

Solving for r:

1 + r = 95.40 / 90
1 + r = 1.06
r = 0.06 or 6%

Therefore, the interest rate that makes the present value of $95.40 one year from today equal to $90 today is 6 percent.

Question 10

At which interest rate is the present value of $196.85 three years from today equal to $175 today?
A) 2 percent
B) 4 percent
C) 6 percent
D) 8 percent

Accepted Answer

The answer of At which interest rate is the present...

Question 11

Which of the following changes would decrease the present value of a future payment?
A) a decrease in the size of the payment
B) an increase in the time until the payment is made
C) an increase in the interest rate
D) All of the above are correct.

Accepted Answer

A decrease in the size of the payment means less money to be received in the future, which would decrease its present value. An increase in the time until the payment is made means a longer wait for the money to be received, which would also decrease its present value. An increase in the interest rate would increase the discount rate used to calculate the present value, which would also decrease the present value of the future payment. Therefore, all of these changes would decrease the present value of a future payment.

Question 12

Sage decides to cash in all his savings to open a recording studio. He has three accounts to cash in. The first earned 9 percent for two years. The second earned 6 percent for three years. And the last earned 3 percent for six years. Supposing he started with $5,000 in each account, from which account will he get the most cash?
A) the two-year account at 9 percent
B) the three-year account at 6 percent
C) the six-year account at 3 percent
D) The accounts are all worth the same.

Accepted Answer

The answer of Sage decides to cash in all his...

Question 13

What is the present value of a payment of $100 to be made one year from today?
A) $100*(1 + r)
B) $100/(1 + r)
C) $100 - $100  r
D) $100 - (1 + r)/$100

Accepted Answer

The present value formula for a single payment is PV = FV/(1+r). In this case, FV is $100 and r is the interest rate. Therefore, the present value would be $100/(1+r).

Question 14

The present value of a payment to be made in the future falls as
A) the interest rate rises and the time until the payment is made increases.
B) the interest rate rises and the time until the payment is made decreases.
C) the interest rate falls and the time until the payment is made increases.
D) the interest rate falls and the time until the payment is made decreases.

Accepted Answer

The answer of The present value of a payment to...

Question 15

You are expecting to receive $750 at some time in the future. Which of the following would unambiguously decrease the present value of this future payment?
A) Interest rates rise and you get the payment sooner.
B) Interest rates rise and you have to wait longer for the payment.
C) Interest rates fall and you get the payment sooner.
D) Interest rates fall and you have to wait longer to get the payment.

Accepted Answer

The answer of You are expecting to receive $750 at...

Question 16

A scholarship gives you $1,000 today and promises to pay you $1,000 one year from today. What is the present value of these payments? A) $2,000/(1 + r)². B) $1,000 + $1,000/(1 + r) C) $1,000/(1 + r) + $1,000/(1 + r)² D) $1,000(1 + r) + $1,000(1 + r)²

Accepted Answer

The answer of A scholarship gives you $1,000 today and...

Question 17

Al, Ralph, and Stan are all intending to retire. Each currently has $1 million in assets. Al will earn 16% interest and retire in two years. Ralph will earn 8% interest and retire in four years. Stan will earn 4% interest and retire in eight years. Who will have the largest sum when he retires?
A) Al
B) Ralph
C) Stan
D) They all retire with the same amount.

Accepted Answer

The answer of Al, Ralph, and Stan are all intending...

Question 18

You have been promised a payment of $250,000 in the future. In which case is the present value of this payment highest?
A) You receive the payment 3 years from now and the interest rate is 8 percent.
B) You receive the payment 3 years from now and the interest rate is 6 percent.
C) You receive the payment 2 years from now and the interest rate is 8 percent.
D) You receive the payment 2 years from now and the interest rate is 6 percent.

Accepted Answer

The answer of You have been promised a payment of...

Question 19

Which of the following changes would increase the present value of a future payment?
A) a decrease in the size of the payment
B) an increase in the time until the payment is made
C) a decrease in the interest rate
D) All of the above are correct.

Accepted Answer

The answer of Which of the following changes would increase...

Question 20

Which of the following changes would decrease the present value of a future payment?
A) an increase in the size of the payment
B) an increase in the time until the payment is made
C) a decrease in the interest rate
D) All of the above are correct.

Accepted Answer

The present value of a future payment is inversely related to the time until the payment is made. Therefore, an increase in the time until the payment is made would decrease the present value of the payment. A is incorrect because an increase in the size of the payment would increase the present value. C is incorrect because a decrease in the interest rate would also increase the present value.

Quiz 27: The Basic Tools of Finance

At which interest rate is the present value of $168.54 two years from today equal to $150 today?

You are expecting to receive $3,500 at some time in the future. Which of the following would unambiguously increase the present value of this future payment?

Which of the following is the correct expression for finding the present value of a $1,000 payment one year from today if the interest rate is 6 percent?

You want to have $100,000 in five years. If the interest rate is 8 percent, about how much do you need to have today?

At which interest rate is the present value of $80.25 one year from today equal to $75 today?

What is the present value of a payment of $100 one year from today if the interest rate is 5 percent?

Which of the following is the correct expression for finding the present value of a $500 payment two years from today if the interest rate is 6 percent?

You have been promised a payment of $400 in the future. In which of the following cases is the present value of this payment the lowest?

At which interest rate is the present value of $95.40 one year from today equal to $90 today?

At which interest rate is the present value of $196.85 three years from today equal to $175 today?

Which of the following changes would decrease the present value of a future payment?

What is the present value of a payment of $100 to be made one year from today?

The present value of a payment to be made in the future falls as

You are expecting to receive $750 at some time in the future. Which of the following would unambiguously decrease the present value of this future payment?

A scholarship gives you $1,000 today and promises to pay you $1,000 one year from today. What is the present value of these payments?

Al, Ralph, and Stan are all intending to retire. Each currently has $1 million in assets. Al will earn 16% interest and retire in two years. Ralph will earn 8% interest and retire in four years. Stan will earn 4% interest and retire in eight years. Who will have the largest sum when he retires?

You have been promised a payment of $250,000 in the future. In which case is the present value of this payment highest?

Which of the following changes would increase the present value of a future payment?

Which of the following changes would decrease the present value of a future payment?