Optimizing Net Present Value Using Continuous Compounding

The value of good wine increases with age. Thus if you are a wine dealer, you have the problem of deciding whether to sell you wine now, at a price of $P a bottle, or sell it later at a higher price. Suppose you know that the amount a wine-drinker is willing to pay for a bottle of wine t years from now is $P(1+20(sqr(t))). Assuming continuous compounding and a prevailing interest rate of 5% per year, when is the best time to sell your wine?

Solution Preview

The goal is to maximize the net present value of the sale of the wine.
Revenue is given in the question

Revenue = P * (1 + 20 sqrt(t))

Revenue must be discounted by the time value of money, in this case 5% compounded continuously. This discount factor is ...

Solution Summary

The solution provides a detailed look at optimizing the Net Present Value of an appreciating asset. The solution uses continuous compounding to discount the future cash flow. Basic concepts of differential calculus as used as well as solving quadratic equations.

At a 12 percent rate of interest, usingcontinuouscompounding, which of the following three options has the highest presentvalue:
Value Now Value in 1 Year Value in 2 Years
A 0 0 230
B 0 100 110
C 100

Show the formula used in the following questions in detail
1)
a. What is the future value of $4,000 invested at 6% for 22 years with annual compounding?
b. What is the future value of $4,000 invested at 6% for 22 years with monthly compounding?
c. What is the future value of $4,000 invested at 6% for 22 years with cont

The 6-month, 12-month, 18-month, and 24-month zero rates are 3%, 3.5%, 3.75%, and 4% with semi-annual compounding.
Q1: What are the rates with continuouscompounding?
Q2: What is the forward rate for the six-month period beginning in 18 months?

Suppose $1000000.00 will be recieved after 25 years. Find the value 5 years from now (t=5), V(5), assuming continuouscompounding at the rate
r(t) = 0.05 + t/1000 if t<=10 and 0.06 t >10.
I know the answer is 304982.77, but can not get it to work out. Please show all of your work.

25. The stated rate of interest is 10%. Which form of compounding will give the highest effective rate of interest?
A. annual compounding
B. monthly compounding
C. daily compounding
D. continuouscompounding
E. It is impossible to tell without knowing the term of the loan.

How much difference does it make for a bank account whether there is continuouscompounding of interest, or monthly or annual compounding?
Using the below information:
$2000 deposited in account
interest rate of 2.25%

Which amounts represents the end value of investing $80,000 for 3 years at a continuously compounded rate of 12%?
I am not sure how to calculate a problem which has continuouscompounding - I know you have to use the e function, but I do not understand or know how.. Can I just substitute the value of e into the forumla?

How much difference do you think it makes for your bank account whether there is continuouscompounding of interest, or only monthly or annual compounding? Do you ever try to make the interest calculations yourself for the interest you earned?

suppose the deposit $20,000 for 5 yrs @ 8% rate what is the return annually (n = 1) and quarterly (n = 4).
Round both to the hundredth place.
c) Does compounding annually or quarterly yield more interest and explain
d) if a bank compounds continuously the the formula used is A=Pe^rt where e is a constant and equals