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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.


Answer:


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.


Answer:


Show work in this space:


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.


Answer:
 
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1 Answer

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