Deck 6: A Continuous-Compounding-And-Discounting

Question 1

You place $1,000 in an account that pays 7.00% interest compounded continuously.You plan to hold the account exactly 3 years.Simultaneously,in another account you deposit money that earns 5.20% compounded semiannually.If the accounts are to have the same amount at the end of the 3 years,how much of an initial deposit do you need to make now in the account that pays 5.20% interest compounded semiannually? Do not round your intermediate calculations.

A) $1,025.86
B) $803.77
C) $1,057.59
D) $1,290.26
E) $835.50

Answer 1

C

Question 2

In six years' time,you are scheduled to receive money from a trust established by your grandparents.When the trust matures there will be $100,000 in the account.If the account earns 10.50% compounded continuously,how much is in the account today?

A) $66,573.98
B) $45,270.30
C) $56,454.73
D) $53,259.18
E) $55,389.55

Answer 2

D

Question 3

Assume one bank offers you a nominal annual interest rate of 6.00% compounded daily while another bank offers you continuous compounding at a 5.90% nominal annual rate.You decide to deposit $1,250 with each bank.Exactly two years later you withdraw your funds from both banks.What is the difference in your withdrawal amounts between the two banks? Assume 365 days in a year.Do not round your intermediate calculations.

A) $2.66
B) $2.10
C) $2.80
D) $2.94
E) $2.38

Answer 3

C

Question 4

You have $5,436.60 in an account that pays 10.70% interest,compounded continuously.If you deposited some funds 13 years ago,how much was your original deposit? Round your answer to the nearest dollar.

A) $1,055
B) $1,353
C) $1,082
D) $1,515
E) $1,407

Question 5

For a 10-year deposit,what annual rate payable semiannually will produce the same effective rate as 5.75% compounded continuously? Do not round your intermediate calculations.

A) 5.43%
B) 5.83%
C) 6.53%
D) 6.88%
E) 4.38%

Question 6

How much should you be willing to pay for an account today that will have a value of $1,000 in 7 years under continuous compounding if the nominal rate is 8.30%?

A) $682.39
B) $559.34
C) $425.10
D) $637.65
E) $660.02

Question 7

You need a down payment of $18,400 in order to purchase your first home 4 years from today.You currently have $14,014 to invest.In order to achieve your goal,what nominal interest rate,compounded continuously,must you earn on this investment? Do not round your intermediate calculations.

A) 7.15%
B) 6.81%
C) 7.28%
D) 5.51%
E) 6.26%

Question 8

If you receive $15,000 today and can invest it at a 8.00% annual rate compounded continuously,what will be your ending value after 20 years?

A) $63,894.12
B) $56,464.57
C) $74,295.49
D) $92,869.36
E) $80,982.08