Appendix: Continuous Compounding And Discounting

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Question 1
Free
Multiple Choice

With continuous compounding

Choose correct answer/s
A

the effective rate is higher than the nominal rate

B

the effective rate is higher than the logarithmic rate

C

the base "e" is the effective rate

D

all the above are correct

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Question 2
Free
Multiple Choice

In the continuous compounding equation, "e" is the

Choose correct answer/s
A

natural log to the base 10.

B

base number in natural logarithms

C

natural log to the base 1.

D

none of the above are correct

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Question 3
Free
Multiple Choice

Determine the value of $10,000 at the end of 3 years invested at 8 percent assuming continuous compounding.

Choose correct answer/s
A

$12,712

B

$12,400

C

$32,460

D

$12,600

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Question 4
Free
Multiple Choice

Determine the present value of $5,000 to be received 4 years from now at the continuously discounted rate of 8 percent.

Choose correct answer/s
A

$6,886

B

$3,631

C

$4,616

D

None of the above

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Question 5
Free
Multiple Choice

First Texas National Bank is offering a one-year CD with a nominal rate of 9.5 percent. If compounding occurs continuously, what is the effective annual rate?

Choose correct answer/s
A

9.97%

B

16.76%

C

9.66%

D

22.06%

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Question 6
Multiple Choice

What is the future value of $20,000 invested for 20 years at a nominal interest rate of 9 percent compounded continuously?

Choose correct answer/s
A
$112,088
B
$120,993
C
$108,894
D
$147,781
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Question 7
Multiple Choice

Calculate the effective annual rate if the nominal annual rate is 9 percent compounded continuously.

Choose correct answer/s
A
9.74%
B
9.29%
C
9.42%
D
9.54%
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Question 8
Multiple Choice

What is the present value of $100,000 that will be received 20 years from now if the nominal discount rate is 11 percent, discounted continuously?

Choose correct answer/s
A
$21,240
B
$11,080
C
$16,421
D
none of the above
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Question 9
Multiple Choice

You have just won a lottery that promises to pay you $1,000,000 in 5 years. What is the present value of this lottery win at the continuously discounted rate of 10%?

Choose correct answer/s
A
$621,000
B
$606,531
C
$648,720
D
$904,837
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Question 10
Multiple Choice

Fred deposited $5,000 in an account that promised a nominal interest rate of 8% compounded continuously for his daughter who will be going to college in 18 years. How much will she have in the account in 18 years?

Choose correct answer/s
A
$19,980
B
$20,054
C
$21,103
D
$21,694
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Question 11
Multiple Choice

Vida has just won a jackpot that will pay her $10,000 now, $10,000 in one year, and $10,000 in 2 years. What is the present value of this jackpot at the continuously discounted rate of 9%?

Choose correct answer/s
A
$27,515
B
$28,345
C
$24,516
D
$27,492
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Question 12
Multiple Choice

City Bank offers a 7 year CD with a nominal rate of interest of 7.0%. If compounding occurs continuously, what is the effective annual rate?

Choose correct answer/s
A
7.25%
B
6.77%
C
7.32%
D
7.00%
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Question 13
Multiple Choice

What continuously compounded effective rate of interest will yield the same present value of a future cash flow as an annual rate of interest of 8.25%?

Choose correct answer/s
A
8.60%
B
7.93%
C
8.25%
D
7.70%
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Question 14
Multiple Choice

What is the value of $10,000 invested for 1 year at 8% compounded continuously?

Choose correct answer/s
A
$10,800
B
$10,833
C
$10,824
D
$11,268
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Question 15
Multiple Choice

What is the value of $10,000 invested for 5 years at 8% compounded continuously?

Choose correct answer/s
A
$14,693
B
$14,928
C
$14,918
D
$13,064
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Question 16
Multiple Choice

Friendly Bank offers you a loan at an annual interest rate of 10% compounded monthly. What is the effective rate the bank is charging you?

Choose correct answer/s
A
12.68%
B
10.00%
C
10.47%
D
10.83%
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Question 17
Multiple Choice

Jane deposited $1000 into a saving account paying 12% interest compounded continuously. After 45 years, how much money did she have in the account?

Choose correct answer/s
A
$25, 759.09
B
$157,896.32
C
$221,406.42
D
$257,895.78
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Question 18
Multiple Choice

Paula invested $25 into a savings account when she was 6 years old. She is now 35. Her money grew at 2% compounded continuously. How much money does she have?

Choose correct answer/s
A
$106.58
B
$85.19
C
$270.82
D
$44.65
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Question 19
Multiple Choice

Jack invested $25,000 into an account paying 6% compounded continuously. In five years how much money will he have?

Choose correct answer/s
A
$92,190.45
B
$215,905.42
C
$65,871.15
D
$33,746.47
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Question 20
Multiple Choice

If interest is at 8% and it is compounded continuously, what is the effective interest rate?

Choose correct answer/s
A
7.25%
B
5.14%
C
8.33%
D
9.76%
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