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# Logarithmic functions explained in this solution

The formula for calculating the amount of money returned for an initial deposit money into a bank account or CD (Certificate of Deposit) is given by

A is the amount of returned.
P is the principal amount initially 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 \$10,000 for 2 years at a rate of 10%.

a)Calculate the return (A) if the bank compounds annually (n = 1).

Use ^ to indicate the power.

b) Calculate the return (A) if the bank compounds quarterly (n = 4).

c) Calculate the return (A) if the bank compounds monthly (n = 12).

d) Calculate the return (A) if the bank compounds daily (n = 365).

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 takes a simpler, that is

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 \$15,000 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 10% interest rate and continuous compounding, what is the answer?

#### Solution Preview

Logarithmic Functions
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The formula for calculating the amount of money returned for an initial deposit money into a bank account or CD (Certificate of Deposit) is given by

A is the amount of returned.
P is the principal amount initially 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 \$10,000 for 2 years at a rate of 10%.
a)Calculate the return (A) if the bank compounds annually (n = 1).

#### Solution Summary

This solution is comprised of a detailed explanation to calculate the return (A) if the bank compounds annually (n = 1).

\$2.19