SOLUTION: Please Help me with this word problem. This is my last assignment and I am stuck on this, so if you can help I really apreciate it. Thank you The formula for calculation the am

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Question 116745: Please Help me with this word problem. This is my last assignment and I am stuck on this, so if you can help I really apreciate it. Thank you
The formula for calculation the amount of money retuened for an initial deposit into a bank account or CD is given by A=P(1+r/n)
A is the amount of return
P is the principal of intitial deposit
r is 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 round final number to nearest cent.
Suppose you deposit $4000 for 8years at a rate of 7%
A) calculate the return(A) if the bank compounds annually(n=1) round to hundredth place
B)calculate the return(A) if the bank compounds monthly (n=12) round to nearest hundredth place
C) Does compounding annually or monthly yeild more interest? explain why
D)If a bank compounds continuously then the formula used is A=Pe^n where e is a constant and equals approximately 2.7183
Calculate A with continuous compounding. round to nearest hundredth place
E) How long will it take to double my money at 7% interest rate and continuous compounding. round to the nearest Hundredth place
SHOW ALL WORK FOR A-E QUESTIONS THANK YOU AGAIN IN ADVANCE
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Suppose you deposit $4000 for 8years at a rate of 7%
A) calculate the return(A) if the bank compounds annually(n=1) round to hundredth place
A(t) = P(1+r/n)^(nt)
A(8) = 4000(1+0.07/1)^(1*8 =$6872.75
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B)calculate the return(A) if the bank compounds monthly (n=12) round to nearest hundredth place
A(8)= 4000(1+(0.07/12))^(12*8)
A(8)= 4000(1.0058)^(96)= $6969.10
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C) Does compounding annually or monthly yeild more interest? explain why
monthly because, although you compound at a smaller rate, compounding
more ofterm more than offsets the difference.
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D)If a bank compounds continuously then the formula used is A(t)=Pe^rt where e is a constant and equals approximately 2.7183
Calculate A with continuous compounding. round to nearest hundredth place
A(8) = 4000e^(0.07*8)
A(8) = 4000*1.7507
A(8) = $7002.69
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E) How long will it take to double my money at 7% interest rate and continuous compounding. round to the nearest Hundredth place
8000 = 4000e^(0.07t)
2 = e^(0.07t)
0.07t = ln2
t = (ln2)/(0.07)
t = 9.90 years
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Cheers,
Stan H.