Appendix: Continuous Compounding And Discounting

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Question 1
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Multiple Choice

With continuous compounding

the effective rate is higher than the nominal rate

the effective rate is higher than the logarithmic rate

the base "e" is the effective rate

all the above are correct

Question 2
Free
Multiple Choice

In the continuous compounding equation, "e" is the

natural log to the base 10.

base number in natural logarithms

natural log to the base 1.

none of the above are correct

Question 3
Free
Multiple Choice

\$12,712

\$12,400

\$32,460

\$12,600

Question 4
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Multiple Choice

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

\$6,886

\$3,631

\$4,616

None of the above

Question 5
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Multiple Choice

9.97%

16.76%

9.66%

22.06%

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?

\$112,088
\$120,993
\$108,894
\$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.

9.74%
9.29%
9.42%
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?

\$21,240
\$11,080
\$16,421
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%?

\$621,000
\$606,531
\$648,720
\$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?

\$19,980
\$20,054
\$21,103
\$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%?

\$27,515
\$28,345
\$24,516
\$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?

7.25%
6.77%
7.32%
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%?

8.60%
7.93%
8.25%
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?

\$10,800
\$10,833
\$10,824
\$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?

\$14,693
\$14,928
\$14,918
\$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?

12.68%
10.00%
10.47%
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?

\$25, 759.09
\$157,896.32
\$221,406.42
\$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?

\$106.58
\$85.19
\$270.82
\$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?

\$92,190.45
\$215,905.42
\$65,871.15
\$33,746.47
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Question 20
Multiple Choice