CHAPTER 5A
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 the above are correct
2. With continuous compounding
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 these are correct
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
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
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%
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
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%
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
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
Chapter 5A
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
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
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%
c. 7.32%
d. 7.00%
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%
Chapter 5A
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
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
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%
17. Jane deposited $1000 into a saving 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. $221,406.42
d. $257,895.78
Chapter 5A
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?
a. $106.58
b. $85.19
c. $270.82
d. $44.65
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. $33,746.47
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%
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%
22. What is the effective interest rate if 10% is compounded continuously?
a. 10.52%
b. 10.97%
c. 11.06%
d. 10.11%
Chapter 5A
23. Brad deposited $5,250 into an account that earns 7% interest compounded continuously. How much money
will he have in 15 years?
a. $15,002.67
b. $12,175.90
c. $13,957.14
d. $14,964.25
24. Moneybag Bank & Trust is offering loans at 5% compounded continuously. Before you decide to borrow using
that interest rate, what amount would need to be paid back if the loan is for 10 years?
a. $329,744.25
b. $275,187.36
c. $301,150.15
d. $227,198.05
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%
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. .95%
d. 1.28%
Chapter 5A
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.
28. With continuous compounding, why is the effective rate higher than the nominal rate?