Exam 22: Continuous Compounding and Discounting

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?

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?

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%?

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?

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?

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

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?

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?