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## The formula for calculating the amount of money returned for an initial deposit into a bank account or CD (certificate of deposit) is given b

A is the amount of the return.
P is the principal amount initially deposited.
r is the annual interest rate (expressed as a decimal).
n is the number of compound periods in one year.
t is the number of years.

Carry all calculations to six decimals on each intermediate step, then round the final answer to the nearest cent.

Suppose you deposit \$3,000 for 6 years at a rate of 7%.

a) Calculate the return (A) if the bank compounds semi-annually. Round your answer to the nearest cent.

Show work in this space. Use ^ to indicate the power or use the Equation Editor in MS Word.

b) Calculate the return (A) if the bank compounds monthly. Round your answer to the nearest cent.

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c) If a compounds continuously, then the formula used is A=Pe^rt where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the nearest cent.

Show work:

A is the amount of the return.
P is the principal amount initially deposited.
r is the annual interest rate (expressed as a decimal).
n is the number of compound periods in one year.
t is the number of years.

A = P [1 + (r/n)]^nt

Suppose you deposit \$3,000 for 6 years at a rate of 7%.

a) Calculate the return (A) if the bank compounds semi-annually. Round your answer to the nearest cent.

A = (\$3,000)[1 + (0.07/2)]^(2)(6) = (\$3,000)[1 + 0.035]^12 = (\$3,000)(1.035)^12 = \$4,533.21

b) Calculate the return (A) if the bank compounds monthly. Round your answer to the nearest cent.

A = (\$3,000)[1 + (0.07/12)]^(12)(6) =(\$3,000)(12.07/12)^72 = \$4,560.32

c) If a compounds continuously, then the formula used is A=Pe^rt where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding. Round your answer to the nearest cent.

A = (\$3,000)e^rt =  (\$3,000)e^(.07)(6) = (\$3,000)e^0.42 = \$4565.88