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Question 43603: Ok, I've got a real big problem here and i'm thoroughly overwhelmed and confused. Can someone please help. Here's the problem:
The formula for calculating the amount of money returned for an initial deposit money into a back account or CD (Certificate of Deposit) is given by
A = P(1 + r/n)^m.
A is the amount of return
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%. Calculate the return (A) if the bank compounds annual (n=1).
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Show work in space. Use ^ to indicate the power.
Calculate the return (A) if the bank compounds quarterly (n = 4), and carry all calculations to 7 significant figures.
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Calculate the return (A) if the bank compounds monthly (n=12), and carry all calculations to 7 significant figures.
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Calculate the return (A) if the bank compounds daily (n=365), and carry all calculations to 7 significant figures.
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What observation can you make about the increase in your return as your compounding increases more frequently?
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If a bank compounds continuously, then the formula takes a simpler, that is A = Pe^n. Where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding.
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Now suppose, instead of knowing t, we know that the bank returned to us $15,000 with the bank compounding continuously. Using natural logarithms, find how long we left the money in the bank (find f).
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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?
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Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A = P(1 + r/n)^m.
Suppose you deposit $10,000 for 2 years at a rate of 10%. Calculate the return (A) if the bank compounds annual (n=1).
A=10000(1+0.10/1)^2
A=10000*1.21= 12100
Calculate the return (A) if the bank compounds quarterly (n = 4), and carry all calculations to 7 significant figures. (I assume you mean for 2 years)
A=10000(1+0.10/4)^(4*2)
A=10000(1.2184029
A=12184.03
Calculate the return (A) if the bank compounds monthly (n=12), and carry all calculations to 7 significant figures. (I assume you for 2 years)
A=10000(1+0.10/12)^(12*2)
Use your caluculator.
Calculate the return (A) if the bank compounds daily (n=365), and carry all calculations to 7 significant figures. (I assume you mean for two years)
A=10000(1+0.10/365)^(365*2)
Use calculator.
What observation can you make about the increase in your return as your compounding increases more frequently?
That should be obvious.
If a bank compounds continuously, then the formula takes a simpler, that is A = Pe^n. Where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding.
You have to be given the rate and the number of years.
A=Pe^(rn)
A=10000(e^(0.10*?)
Now suppose, instead of knowing t, we know that the bank returned to us $15,000 with the bank compounding continuously. Using natural logarithms, find how long we left the money in the bank (find f).
15000=10000e^(0.10t)
1.5=e^0.10t
ln(1.5)=0.10t
0.40546511...=0.10t
t=4.05 years
"How long will it take to double my money?" At 10% interest rate and continuous compounding
2P=Pe^(0.10t)
2=e^(0.10t)
ln2=0.10t
0.69314718...=0.10t
t=6.93 years
This is generally call "the rule of seven".
Cheers,
Stan H.
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