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Question 37921: Please help I am stuck on this problem :(
3) The formula for calculating the amount of money returned for deposit money into a bank account or CD (Certificate of Deposit) is given by the following:
A=P (1 + r/n)^(nt)
A is the amount of returned
P is the principal amount 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 $20,000 for 3 years at a rate of 8%.
a) Calculate the return (A) if the bank compounds annually (n = 1).
Answer:
Show work in this space. Use ^ to indicate the power.
b) Calculate the return (A) if the bank compounds quarterly (n = 4), and carry all calculations to 7 significant figures.
Answer:
Show work in this space .
c) Calculate the return (A) if the bank compounds monthly (n = 12), and carry all calculations to 7 significant figures.
Answer:
Show work in this space.
d) Calculate the return (A) if the bank compounds daily (n = 365), and carry all calculations to 7 significant figures.
Answer:
Show work in this space.
e) What observation can you make about the increase in your return as your compounding increases more frequently?
Answer:
f) If a bank compounds continuous, then the formula becomes simpler, that is
where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding.
Answer:
Show work in this space
g) Now suppose, instead of knowing t, we know that the bank returned to us $25,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t).
Answer:
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h) A commonly asked question is, “How long will it take to double my money?” At 8% interest rate and continuous compounding, what is the answer?
Answer: Show work in this space
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose you deposit $20,000 for 3 years at a rate of 8%.
a) Calculate the return (A) if the bank compounds annually (n = 1).
Answer:
Show work in this space. Use ^ to indicate the power.
A=20,000(1+0.08/1)^(1)=21600
b) Calculate the return (A) if the bank compounds quarterly (n = 4), and carry all calculations to 7 significant figures.
Answer:
Show work in this space .
A=20000(1+0.08/4)^4=27209.78
c) Calculate the return (A) if the bank compounds monthly (n = 12), and carry all calculations to 7 significant figures.
Answer:
Show work in this space.
A=20000(1+0.08/12)^12=21659.99
d) Calculate the return (A) if the bank compounds daily (n = 365), and carry all calculations to 7 significant figures.
Answer:
Show work in this space.
A=20000(1+0.08/365)^365=21665.55
e) What observation can you make about the increase in your return as your compounding increases more frequently?
Answer:
A increases as compounding times increases.
f) If a bank compounds continuous, then the formula becomes simpler, that is
where e is a constant and equals approximately 2.7183. Calculate A with continuous compounding.
Answer:
Show work in this space
A=e^(rt)
g) Now suppose, instead of knowing t, we know that the bank returned to us $25,000 with the bank compounding continuously. Using logarithms, find how long we left the money in the bank (find t).
Answer:
Show work in this space
25000=20000e^(0.08t)
1.25=e^(0.08t)
Take the natural log of both sides to get:
ln(1.25)=0.08t
0.223/0.08=t
t=2.789
h) A commonly asked question is, “How long will it take to double my money?” At 8% interest rate and continuous compounding, what is the answer?
Answer: Show work in this space
40000=20000e^0.08t
2=e^0.08t
Take the natural log of both sides to get:
0.6931...=0.08t
t=8.66 yrs.
Cheers,
Stan H.
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