Interest and the Time Value of Money : Continuously Compounding Interest
Not what you're looking for?
3) The formula for calculating the amount of money returned for deposit money into a bank account or CD (Certificate of Deposit) is given by the following:
A=P(1+R/N)rt
A is the amount of returned
P is the principal amount deposited
r is the annual interest rate (expressed as a decimal)
n is the compound period
t is the number of years
Suppose you deposit $20,000 for 3 years at a rate of 8%.
a) Calculate the return (A) if the bank compounds annually (n = 1).
b) Calculate the return (A) if the bank compounds quarterly (n = 4), and carry all calculations to 7 significant figures.
c) Calculate the return (A) if the bank compounds monthly (n = 12), and carry all calculations to 7 significant figures
d) Calculate the return (A) if the bank compounds daily (n = 365), and carry all calculations to 7 significant figures.
e) What observation can you make about the increase in your return as your compounding increases more frequently?
f) If a bank compounds continuous, then the formula becomes simpler, that is A=Pe rt
where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding.
g) Now suppose, instead of knowing t, we know that the bank returned to us $25,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t).
h) A commonly asked question is, "How long will it take to double my money?" At 8% interest rate and continuous compounding, what is the answer
Purchase this Solution
Solution Summary
Continuously Compounding Interest is investigated.
Solution Preview
...
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Probability Quiz
Some questions on probability
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.