Question 47673: 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). Round your answer to the hundredth's place.
Answer:
Show work in this space .
c) Calculate the return (A) if the bank compounds monthly (n = 12). Round your answer to the hundredth's place.
Answer:
Show work in this space.
d) Calculate the return (A) if the bank compounds daily (n = 365). Round your answer to the hundredth's place.
Answer:
Show work in this space.
e) What observation can you make about the size of 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. Round your answer to the hundredth's place.
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). Round your answer to the hundredth's place.
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? Round your answer to the hundredth's place.
Answer:
Show work in this space.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A=P(1+r/n)^nt
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).
A=20000(1+0.08/1)^(1(3)= 20000(1.08)^3= $25194.24
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b) Calculate the return (A) if the bank compounds quarterly (n = 4). Round your answer to the hundredth's place.
Same formula. Put 4 in place of n.
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c) Calculate the return (A) if the bank compounds monthly (n = 12). Round your answer to the hundredth's place.
Use 12 in place of n.
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d) Calculate the return (A) if the bank compounds daily (n = 365). Round your answer to the hundredth's place.
Use 365 in place of n
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e) What observation can you make about the size of increase in your return as your compounding increases more frequently?
Answer:
Should be obvious.
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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. Round your answer to the hundredth's place.
Formula for continuous compounding:
A=Pe^(rt)
A=20000e^(0.08(3))
A=20000(1.27124915...)
A=$25424.98
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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). Round your answer to the hundredth's place.
25000=20000e^(0.08t)
1.25=e^0.08t
Take the natural log of both sides to get:
0.08t=0.223143555...
t=2.789... years
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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? Round your answer to the hundredth's place.
If P is doubled the result is 2P.
2P=Pe^0.08t
2=e^0.08t
0.08t=0.69314718...
t=8.66 years.
Cheers,
Stan H.
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