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Multiple Choice
1. In the continuous compounding equation, “e” is the ____.
a.
natural log to the base 10
b.
base number in natural logarithms
c.
natural log to the base 1
d.
None of these are correct
b
2. With continuous compounding, the ____.
a.
effective rate is higher than the nominal rate
b.
effective rate is higher than the logarithmic rate
c.
base “e” is the effective rate
d.
All of these are correct
a
3. Determine the value of $10,000 at the end of 3 years invested at 8 percent assuming continuous compounding.
a.
$12,712
b.
$12,400
c.
$32,460
d.
$12,600
a
4. Determine the present value of $5,000 to be received 4 years from now at the continuously discounted rate of 8 percent.
a.
$6,886
b.
$3,631
c.
$4,616
d.
None of these are correct
b
5. 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?
a.
9.97%
b.
16.76%
c.
9.66%
d.
22.06%
a
6. What is the future value of $20,000 invested for 20 years at a nominal interest rate of 9 percent compounded
continuously?
a.
$112,088
b.
$120,993
c.
$108,894
d.
$147,781
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b
7. Calculate the effective annual rate if the nominal annual rate is 9 percent compounded continuously.
a.
9.74%
b.
9.29%
c.
9.42%
d.
9.54%
c
8. 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?
a.
$21,240
b.
$11,080
c.
$16,421
d.
None of these are correct
b
9. 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%?
a.
$621,000
b.
$606,531
c.
$648,720
d.
$904,837
b
10. 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?
a.
$19,980
b.
$20,054
c.
$21,103
d.
$21,694
c
11. 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%?
a.
$27,515
b.
$28,345
c.
$24,516
d.
$27,492
d
12. 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?
a.
7.25%
b.
6.77%
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c.
7.32%
d.
7.00%
a
13. 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%?
a.
8.60%
b.
7.93%
c.
8.25%
d.
7.70%
b
14. What is the value of $10,000 invested for 1 year at 8% compounded continuously?
a.
$10,800
b.
$10,833
c.
$10,824
d.
$11,268
b
15. What is the value of $10,000 invested for 5 years at 8% compounded continuously?
a.
$14,693
b.
$14,928
c.
$14,918
d.
$13,064
c
16. 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?
a.
12.68%
b.
10.00%
c.
10.47%
d.
10.83%
c
17. Jane deposited $1,000 into a savings account paying 12% interest compounded continuously. After 45 years, how
much money did she have in the account?
a.
$25, 759.09
b.
$157,896.32
c.
$221,405.61
d.
$257,895.78
c
18. 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?
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Class:
Date:
a.
$106.58
b.
$85.19
c.
$270.82
d.
$44.65
d
19. Jack invested $25,000 into an account paying 6% compounded continuously. In five years how much money will he
have?
a.
$92,190.45
b.
$215,905.42
c.
$65,871.15
d.
$33,746.50
d
20. If interest is at 8% and it is compounded continuously, what is the effective interest rate?
a.
7.25%
b.
5.14%
c.
8.33%
d.
9.76%
c
21. What is the effective interest rate on 12% if interest is compounded continuously?
a.
15.11%
b.
16.25%
c.
14.11%
d.
12.75%
d
22. What is the effective interest rate on 10% if interest is compounded continuously?
a.
10.52%
b.
10.97%
c.
11.06%
d.
10.11%
a
23. Brad deposited $5,250 into an account that earns 7% interest compounded continuously. How much money will he
have in 15 years?
a.
$15,002.66
b.
$12,175.90
c.
$13,957.14
d.
$14,964.25
a
24. Moneybag Bank & Trust is offering $200,000 loans at 5% compounded continuously. Before you decide to borrow
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using that interest rate, what amount would need to be paid back if the loan is for 10 years?
a.
$329,744.00
b.
$275,187.36
c.
$301,150.15
d.
$227,198.05
a
25. 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 6.15%?
a.
5.97%
b.
6.32%
c.
4.11%
d.
8.24%
a
26. 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 2.25%?
a.
2.23%
b.
3.15%
c.
0.95%
d.
1.28%
a
27. The nominal interest rate and the effective interest rate are equivalent when compounding occurs ____.
a.
once a year at the end of the year
b.
every quarter
c.
semiannually
d.
monthly
a
Essay
28. With continuous compounding, why is the effective rate higher than the nominal rate?
available to earn its own interest on an on-going basis.