Deck 24: Continuous Compounding and Discounting

Question 1

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%

Answer 1

A
Solution:
Effective rate = e.?? - 1 = 0.0725 or 7.25%

Question 2

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

Answer 2

C
Solution:
FV = $5,000 e?.???¹?? = $21,103.48

Question 3

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 the above

Answer 3

B
Solution:
PV = $100,000/e?.¹¹?²?? = $11,080.32

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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%

Question 9

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 the above

Question 10

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%

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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%

Question 16

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

Question 17

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 the above are correct

Question 18

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%

Question 19

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%

Question 20

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

Question 21

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%

Question 22

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%

Question 23

With continuous compounding, why is the effective rate higher than the nominal rate?

Question 24

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.

Question 25

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%

Question 26

What is the effective interest rate if 10% is compounded continuously?

A) 10.52%
B) 10.97%
C) 11.06%
D) 10.11%

Question 27

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

Question 28

Moneybag Bank & Trust is offering loans at 5% compounded continuously. Before you decide to borrow using that interest rate, what payment would be required on a $200,000 loan for a 30 year loan?

A) $1,089.59
B) $1,578.34
C) $1,183.92
D) $1,226.90