Deck 22: Continuous Compounding and Discounting

Question 1

You need a down payment of $19,000 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?

A)7.61%
B)7.99%
C)8.39%
D)8.81%
E)9.25%

Answer 1

A

Question 2

If you receive $15,000 today and can invest it at a 5% annual rate compounded continuously,what will be your ending value after 20 years?

A)$38,735.52
B)$40,774.23
C)$42,812.94
D)$44,953.59
E)$47,201.27

Answer 2

B

Question 3

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 9% compounded continuously,how much is in the account today?

A)$55,361.08
B)$58,274.83
C)$61,188.57
D)$64,247.99
E)$67,460.39

Answer 3

B

Question 4

Assume one bank offers you a nominal annual interest rate of 6% compounded daily while another bank offers you continuous compounding at a 5.9% nominal annual rate.You decide to deposit $1,000 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?

A)$2.24
B)$2.35
C)$2.47
D)$2.59
E)$2.72

Question 5

For a 10-year deposit,what annual rate payable semiannually will produce the same effective rate as 4% compounded continuously?

A)3.46%
B)3.65%
C)3.84%
D)4.04%
E)4.24%

Question 6

You have $5,436.60 in an account that pays 10% interest,compounded continuously.If you deposited some funds 10 years ago,how much was your original deposit?

A)$1,900
B)$2,000
C)$2,100
D)$2,205
E)$2,315

Question 7

How much should you be willing to pay for an account today that will have a value of $1,000 in 10 years under continuous compounding if the nominal rate is 10%?

A)$349.49
B)$367.88
C)$386.27
D)$405.59
E)$425.87

Question 8

You place $1,000 in an account that pays 7% interest compounded continuously.You plan to hold the account exactly 3 years.Simultaneously,in another account you deposit money that earns 8% 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 8% interest compounded semiannually?

A)$ 835.94
B)$ 879.93
C)$ 926.24
D)$ 974.99
E)$1,023.74