# Time Value of Money - Continuous Compounding

You make deposits of $2 each year for 30 years. The rate of interest that will prevail is 10 percent for the first 20 years and then 12 percent for the remaining period. If the interest rate is compounded continuously, what is the present and future value of these deposits.

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You make deposits of $2 each year for 30 years. The rate of interest that will prevail is 10 percent for the first 20 years and then 12 percent for the remaining period. If the interest rate is compounded continuously, what is the present and future value of these deposits.

Note: The abbreviations have the following meanings

PVIF= Present Value Interest Factor

PVIFA= Present Value Interest Factor for an Annuity

FVIF= Future Value Interest Factor

FVIFA= Future Value Interest Factor for an Annuity

They can be read from tables or calculated using the following equations

PVIFA( n, ...

#### Solution Summary

The solution is comprised of a discussion on the time value of money, and calculations to determine the present and future value of deposits described in the question.

Interest and the Time Value of Money : Continuously Compounding Interest

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

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